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href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_he.wikipedia.org&uselang=he" class=""><span>תרומה לוויקיפדיה</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=%D7%9E%D7%99%D7%95%D7%97%D7%93:%D7%94%D7%A8%D7%A9%D7%9E%D7%94_%D7%9C%D7%97%D7%A9%D7%91%D7%95%D7%9F&returnto=%D7%9C%D7%95%D7%92%D7%A8%D7%99%D7%AA%D7%9D" title="מומלץ ליצור חשבון ולהיכנס אליו, אך אין חובה לעשות זאת" class=""><span>יצירת חשבון</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=%D7%9E%D7%99%D7%95%D7%97%D7%93:%D7%9B%D7%A0%D7%99%D7%A1%D7%94_%D7%9C%D7%97%D7%A9%D7%91%D7%95%D7%9F&returnto=%D7%9C%D7%95%D7%92%D7%A8%D7%99%D7%AA%D7%9D" title="מומלץ להיכנס לחשבון, אך אין חובה לעשות זאת [o]" accesskey="o" class=""><span>כניסה לחשבון</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="אפשרויות נוספות" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="כלים אישיים" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">כלים אישיים</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="תפריט משתמש" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_he.wikipedia.org&uselang=he"><span>תרומה לוויקיפדיה</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%D7%9E%D7%99%D7%95%D7%97%D7%93:%D7%94%D7%A8%D7%A9%D7%9E%D7%94_%D7%9C%D7%97%D7%A9%D7%91%D7%95%D7%9F&returnto=%D7%9C%D7%95%D7%92%D7%A8%D7%99%D7%AA%D7%9D" title="מומלץ ליצור חשבון ולהיכנס אליו, אך אין חובה לעשות זאת"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>יצירת חשבון</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%D7%9E%D7%99%D7%95%D7%97%D7%93:%D7%9B%D7%A0%D7%99%D7%A1%D7%94_%D7%9C%D7%97%D7%A9%D7%91%D7%95%D7%9F&returnto=%D7%9C%D7%95%D7%92%D7%A8%D7%99%D7%AA%D7%9D" title="מומלץ להיכנס לחשבון, אך אין חובה לעשות זאת [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>כניסה לחשבון</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> דפים לעורכים שלא נכנסו לחשבון <a href="/wiki/%D7%A2%D7%96%D7%A8%D7%94:%D7%91%D7%A8%D7%95%D7%9B%D7%99%D7%9D_%D7%94%D7%91%D7%90%D7%99%D7%9D" aria-label="מידע נוסף על עריכה"><span>מידע נוסף</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/%D7%9E%D7%99%D7%95%D7%97%D7%93:%D7%94%D7%AA%D7%A8%D7%95%D7%9E%D7%95%D7%AA_%D7%A9%D7%9C%D7%99" title="רשימת העריכות שנעשו מכתובת IP זו [y]" accesskey="y"><span>תרומות</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/%D7%9E%D7%99%D7%95%D7%97%D7%93:%D7%94%D7%A9%D7%99%D7%97%D7%94_%D7%A9%D7%9C%D7%99" title="דיון על העריכות שנעשו מכתובת IP זו [n]" accesskey="n"><span>שיחה</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"><div id="mw-dismissablenotice-anonplace"></div><script>(function(){var node=document.getElementById("mw-dismissablenotice-anonplace");if(node){node.outerHTML="\u003Cdiv class=\"mw-dismissable-notice\"\u003E\u003Cdiv class=\"mw-dismissable-notice-close\"\u003E[\u003Ca tabindex=\"0\" role=\"button\"\u003Eהסתרה\u003C/a\u003E]\u003C/div\u003E\u003Cdiv class=\"mw-dismissable-notice-body\"\u003E\u003C!-- CentralNotice --\u003E\u003Cdiv id=\"localNotice\" data-nosnippet=\"\"\u003E\u003Cdiv class=\"anonnotice\" lang=\"he\" dir=\"rtl\"\u003E\u003Cp\u003E\u003Cb\u003Eתמיד רציתם לכתוב בוויקיפדיה אבל לא ידעתם איך? אתם מוזמנים לסדנת עריכה בוויקיפדיה. הסדנה תתקיים בספרייה הלאומית (בבניינה החדש) בירושלים ביום שישי, 06.12.24, בשעה 09:00. להרשמה לחצו \u003Ca href=\"/wiki/%D7%95%D7%99%D7%A7%D7%99%D7%A4%D7%93%D7%99%D7%94:%D7%9E%D7%99%D7%96%D7%9E%D7%99_%D7%95%D7%99%D7%A7%D7%99%D7%A4%D7%93%D7%99%D7%94/%D7%92%D7%9C%D7%90%D7%9D/%D7%94%D7%A1%D7%A4%D7%A8%D7%99%D7%99%D7%94_%D7%94%D7%9C%D7%90%D7%95%D7%9E%D7%99%D7%AA/%D7%90%D7%99%D7%A8%D7%95%D7%A2%D7%99%D7%9D/%D7%A1%D7%93%D7%A0%D7%AA_%D7%A2%D7%A8%D7%99%D7%9B%D7%94_%D7%93%D7%A6%D7%9E%D7%91%D7%A8_2024\" title=\"ויקיפדיה:מיזמי ויקיפדיה/גלאם/הספרייה הלאומית/אירועים/סדנת עריכה דצמבר 2024\"\u003Eכאן\u003C/a\u003E.\u003C/b\u003E\n\u003C/p\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E";}}());</script></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="אתר"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="תוכן עניינים" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">תוכן עניינים</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">העברה לסרגל הצד</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">הסתרה</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">התחלה</div> </a> </li> <li id="toc-הגדרה" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#הגדרה"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>הגדרה</span> </div> </a> <ul id="toc-הגדרה-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-רקע_היסטורי" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#רקע_היסטורי"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>רקע היסטורי</span> </div> </a> <ul id="toc-רקע_היסטורי-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-חוקי_הלוגריתמים" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#חוקי_הלוגריתמים"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>חוקי הלוגריתמים</span> </div> </a> <ul id="toc-חוקי_הלוגריתמים-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-שיטות_לחישוב_לוגריתמים" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#שיטות_לחישוב_לוגריתמים"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>שיטות לחישוב לוגריתמים</span> </div> </a> <button aria-controls="toc-שיטות_לחישוב_לוגריתמים-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>שינוי מצב התת־פרק שיטות לחישוב לוגריתמים</span> </button> <ul id="toc-שיטות_לחישוב_לוגריתמים-sublist" class="vector-toc-list"> <li id="toc-האלגוריתם_של_פיינמן" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#האלגוריתם_של_פיינמן"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>האלגוריתם של פיינמן</span> </div> </a> <ul id="toc-האלגוריתם_של_פיינמן-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-הממוצע_האריתמטי-גאומטרי" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#הממוצע_האריתמטי-גאומטרי"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>הממוצע האריתמטי-גאומטרי</span> </div> </a> <ul id="toc-הממוצע_האריתמטי-גאומטרי-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-ראו_גם" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#ראו_גם"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>ראו גם</span> </div> </a> <ul id="toc-ראו_גם-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-קישורים_חיצוניים" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#קישורים_חיצוניים"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>קישורים חיצוניים</span> </div> </a> <ul id="toc-קישורים_חיצוניים-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="תוכן עניינים" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="מצב תוכן העניינים" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">מצב תוכן העניינים</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">לוגריתם</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="מעבר לערך בשפה אחרת. זמין ב־109 שפות" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-109" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">109 שפות</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-en badge-Q17437796 badge-featuredarticle mw-list-item" title="ערך מומלץ"><a href="https://en.wikipedia.org/wiki/Logarithm" title="Logarithm – אנגלית" lang="en" hreflang="en" data-title="Logarithm" data-language-autonym="English" data-language-local-name="אנגלית" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Logaritme" title="Logaritme – אפריקאנס" lang="af" hreflang="af" data-title="Logaritme" data-language-autonym="Afrikaans" data-language-local-name="אפריקאנס" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Logarithmus" title="Logarithmus – גרמנית שווייצרית" lang="gsw" hreflang="gsw" data-title="Logarithmus" data-language-autonym="Alemannisch" data-language-local-name="גרמנית שווייצרית" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%88%8E%E1%8C%8B%E1%88%AA%E1%8B%9D%E1%88%9D" title="ሎጋሪዝም – אמהרית" lang="am" hreflang="am" data-title="ሎጋሪዝም" data-language-autonym="አማርኛ" data-language-local-name="אמהרית" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Logaritmo" title="Logaritmo – אראגונית" lang="an" hreflang="an" data-title="Logaritmo" data-language-autonym="Aragonés" data-language-local-name="אראגונית" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%84%D9%88%D8%BA%D8%A7%D8%B1%D9%8A%D8%AA%D9%85" title="لوغاريتم – ערבית" lang="ar" hreflang="ar" data-title="لوغاريتم" data-language-autonym="العربية" data-language-local-name="ערבית" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ary mw-list-item"><a href="https://ary.wikipedia.org/wiki/%D9%84%D9%88%DA%AD%D8%A7%D8%B1%D9%8A%D8%AA%D9%85" title="لوڭاريتم – מרוקאית" lang="ary" hreflang="ary" data-title="لوڭاريتم" data-language-autonym="الدارجة" data-language-local-name="מרוקאית" class="interlanguage-link-target"><span>الدارجة</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%98%E0%A6%BE%E0%A6%A4%E0%A6%BE%E0%A6%82%E0%A6%95" title="ঘাতাংক – אסאמית" lang="as" hreflang="as" data-title="ঘাতাংক" data-language-autonym="অসমীয়া" data-language-local-name="אסאמית" class="interlanguage-link-target"><span>অসমীয়া</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Logaritmu" title="Logaritmu – אסטורית" lang="ast" hreflang="ast" data-title="Logaritmu" data-language-autonym="Asturianu" data-language-local-name="אסטורית" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Loqarifm" title="Loqarifm – אזרית" lang="az" hreflang="az" data-title="Loqarifm" data-language-autonym="Azərbaycanca" data-language-local-name="אזרית" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%9B%D0%BE%D0%B3%D0%B0%D1%80%D0%B8%D1%84%D0%BC" title="Логарифм – בשקירית" lang="ba" hreflang="ba" data-title="Логарифм" data-language-autonym="Башҡортса" data-language-local-name="בשקירית" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-bat-smg mw-list-item"><a href="https://bat-smg.wikipedia.org/wiki/Luogar%C4%97tmos" title="Luogarėtmos – זאמוטית" lang="sgs" hreflang="sgs" data-title="Luogarėtmos" data-language-autonym="Žemaitėška" data-language-local-name="זאמוטית" class="interlanguage-link-target"><span>Žemaitėška</span></a></li><li class="interlanguage-link interwiki-bcl mw-list-item"><a href="https://bcl.wikipedia.org/wiki/Logaritmo" title="Logaritmo – ביקולית מרכזית" lang="bcl" hreflang="bcl" data-title="Logaritmo" data-language-autonym="Bikol Central" data-language-local-name="ביקולית מרכזית" class="interlanguage-link-target"><span>Bikol Central</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9B%D0%B0%D0%B3%D0%B0%D1%80%D1%8B%D1%84%D0%BC" title="Лагарыфм – בלארוסית" lang="be" hreflang="be" data-title="Лагарыфм" data-language-autonym="Беларуская" data-language-local-name="בלארוסית" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%9B%D1%8F%D0%B3%D0%B0%D1%80%D1%8B%D1%82%D0%BC" title="Лягарытм – בלארוסית טרשקביץ׳" lang="be-tarask" hreflang="be-tarask" data-title="Лягарытм" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="בלארוסית טרשקביץ׳" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9B%D0%BE%D0%B3%D0%B0%D1%80%D0%B8%D1%82%D1%8A%D0%BC" title="Логаритъм – בולגרית" lang="bg" hreflang="bg" data-title="Логаритъм" data-language-autonym="Български" data-language-local-name="בולגרית" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bjn mw-list-item"><a href="https://bjn.wikipedia.org/wiki/Logaritma" title="Logaritma – בנג׳רית" lang="bjn" hreflang="bjn" data-title="Logaritma" data-language-autonym="Banjar" data-language-local-name="בנג׳רית" class="interlanguage-link-target"><span>Banjar</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%B2%E0%A6%97%E0%A6%BE%E0%A6%B0%E0%A6%BF%E0%A6%A6%E0%A6%AE" title="লগারিদম – בנגלית" lang="bn" hreflang="bn" data-title="লগারিদম" data-language-autonym="বাংলা" data-language-local-name="בנגלית" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-br mw-list-item"><a href="https://br.wikipedia.org/wiki/Logaritm" title="Logaritm – ברטונית" lang="br" hreflang="br" data-title="Logaritm" data-language-autonym="Brezhoneg" data-language-local-name="ברטונית" class="interlanguage-link-target"><span>Brezhoneg</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Logaritam" title="Logaritam – בוסנית" lang="bs" hreflang="bs" data-title="Logaritam" data-language-autonym="Bosanski" data-language-local-name="בוסנית" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-bxr mw-list-item"><a href="https://bxr.wikipedia.org/wiki/%D0%9B%D0%BE%D0%B3%D0%B0%D1%80%D0%B8%D1%84%D0%BC" title="Логарифм – בוריאטית" lang="bxr" hreflang="bxr" data-title="Логарифм" data-language-autonym="Буряад" data-language-local-name="בוריאטית" class="interlanguage-link-target"><span>Буряад</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Logaritme" title="Logaritme – קטלאנית" lang="ca" hreflang="ca" data-title="Logaritme" data-language-autonym="Català" data-language-local-name="קטלאנית" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D9%84%DB%86%DA%AF%D8%A7%D8%B1%DB%8C%D8%AA%D9%85" title="لۆگاریتم – כורדית סוראנית" lang="ckb" hreflang="ckb" data-title="لۆگاریتم" data-language-autonym="کوردی" data-language-local-name="כורדית סוראנית" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Logaritmus" title="Logaritmus – צ׳כית" lang="cs" hreflang="cs" data-title="Logaritmus" data-language-autonym="Čeština" data-language-local-name="צ׳כית" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%9B%D0%BE%D0%B3%D0%B0%D1%80%D0%B8%D1%84%D0%BC" title="Логарифм – צ׳ובשית" lang="cv" hreflang="cv" data-title="Логарифм" data-language-autonym="Чӑвашла" data-language-local-name="צ׳ובשית" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Logarithm" title="Logarithm – ולשית" lang="cy" hreflang="cy" data-title="Logarithm" data-language-autonym="Cymraeg" data-language-local-name="ולשית" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Logaritme" title="Logaritme – דנית" lang="da" hreflang="da" data-title="Logaritme" data-language-autonym="Dansk" data-language-local-name="דנית" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Logarithmus" title="Logarithmus – גרמנית" lang="de" hreflang="de" data-title="Logarithmus" data-language-autonym="Deutsch" data-language-local-name="גרמנית" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-diq mw-list-item"><a href="https://diq.wikipedia.org/wiki/Logaritma" title="Logaritma – זזקית" lang="diq" hreflang="diq" data-title="Logaritma" data-language-autonym="Zazaki" data-language-local-name="זזקית" class="interlanguage-link-target"><span>Zazaki</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9B%CE%BF%CE%B3%CE%AC%CF%81%CE%B9%CE%B8%CE%BC%CE%BF%CF%82" title="Λογάριθμος – יוונית" lang="el" hreflang="el" data-title="Λογάριθμος" data-language-autonym="Ελληνικά" data-language-local-name="יוונית" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-eml mw-list-item"><a href="https://eml.wikipedia.org/wiki/Logar%C3%ACtem" title="Logarìtem – אמיליאנית רומניולית" lang="egl" hreflang="egl" data-title="Logarìtem" data-language-autonym="Emiliàn e rumagnòl" data-language-local-name="אמיליאנית רומניולית" class="interlanguage-link-target"><span>Emiliàn e rumagnòl</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Logaritmo" title="Logaritmo – אספרנטו" lang="eo" hreflang="eo" data-title="Logaritmo" data-language-autonym="Esperanto" data-language-local-name="אספרנטו" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Logaritmo" title="Logaritmo – ספרדית" lang="es" hreflang="es" data-title="Logaritmo" data-language-autonym="Español" data-language-local-name="ספרדית" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Logaritm" title="Logaritm – אסטונית" lang="et" hreflang="et" data-title="Logaritm" data-language-autonym="Eesti" data-language-local-name="אסטונית" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Logaritmo" title="Logaritmo – בסקית" lang="eu" hreflang="eu" data-title="Logaritmo" data-language-autonym="Euskara" data-language-local-name="בסקית" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-ext mw-list-item"><a href="https://ext.wikipedia.org/wiki/Logaritmu" title="Logaritmu – אקסטרמדורית" lang="ext" hreflang="ext" data-title="Logaritmu" data-language-autonym="Estremeñu" data-language-local-name="אקסטרמדורית" class="interlanguage-link-target"><span>Estremeñu</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%84%DA%AF%D8%A7%D8%B1%DB%8C%D8%AA%D9%85" title="لگاریتم – פרסית" lang="fa" hreflang="fa" data-title="لگاریتم" data-language-autonym="فارسی" data-language-local-name="פרסית" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Logaritmi" title="Logaritmi – פינית" lang="fi" hreflang="fi" data-title="Logaritmi" data-language-autonym="Suomi" data-language-local-name="פינית" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fo mw-list-item"><a href="https://fo.wikipedia.org/wiki/Logaritma" title="Logaritma – פארואזית" lang="fo" hreflang="fo" data-title="Logaritma" data-language-autonym="Føroyskt" data-language-local-name="פארואזית" class="interlanguage-link-target"><span>Føroyskt</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Logarithme" title="Logarithme – צרפתית" lang="fr" hreflang="fr" data-title="Logarithme" data-language-autonym="Français" data-language-local-name="צרפתית" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Logartam" title="Logartam – אירית" lang="ga" hreflang="ga" data-title="Logartam" data-language-autonym="Gaeilge" data-language-local-name="אירית" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gan mw-list-item"><a href="https://gan.wikipedia.org/wiki/%E5%B0%8D%E6%95%B8" title="對數 – סינית גאן" lang="gan" hreflang="gan" data-title="對數" data-language-autonym="贛語" data-language-local-name="סינית גאן" class="interlanguage-link-target"><span>贛語</span></a></li><li class="interlanguage-link interwiki-gcr mw-list-item"><a href="https://gcr.wikipedia.org/wiki/Logaritm" title="Logaritm – קראולית גוויאנית" lang="gcr" hreflang="gcr" data-title="Logaritm" data-language-autonym="Kriyòl gwiyannen" data-language-local-name="קראולית גוויאנית" class="interlanguage-link-target"><span>Kriyòl gwiyannen</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Logaritmo" title="Logaritmo – גליסית" lang="gl" hreflang="gl" data-title="Logaritmo" data-language-autonym="Galego" data-language-local-name="גליסית" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B2%E0%A4%98%E0%A5%81%E0%A4%97%E0%A4%A3%E0%A4%95" title="लघुगणक – הינדי" lang="hi" hreflang="hi" data-title="लघुगणक" data-language-autonym="हिन्दी" data-language-local-name="הינדי" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hif mw-list-item"><a href="https://hif.wikipedia.org/wiki/Logarithm" title="Logarithm – הינדית פיג׳ית" lang="hif" hreflang="hif" data-title="Logarithm" data-language-autonym="Fiji Hindi" data-language-local-name="הינדית פיג׳ית" class="interlanguage-link-target"><span>Fiji Hindi</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Logaritam" title="Logaritam – קרואטית" lang="hr" hreflang="hr" data-title="Logaritam" data-language-autonym="Hrvatski" data-language-local-name="קרואטית" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu badge-Q17437796 badge-featuredarticle mw-list-item" title="ערך מומלץ"><a href="https://hu.wikipedia.org/wiki/Logaritmus" title="Logaritmus – הונגרית" lang="hu" hreflang="hu" data-title="Logaritmus" data-language-autonym="Magyar" data-language-local-name="הונגרית" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%BC%D5%B8%D5%A3%D5%A1%D6%80%D5%AB%D5%A9%D5%B4" title="Լոգարիթմ – ארמנית" lang="hy" hreflang="hy" data-title="Լոգարիթմ" data-language-autonym="Հայերեն" data-language-local-name="ארמנית" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Logarithmo" title="Logarithmo – ‏אינטרלינגואה" lang="ia" hreflang="ia" data-title="Logarithmo" data-language-autonym="Interlingua" data-language-local-name="‏אינטרלינגואה" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Logaritma" title="Logaritma – אינדונזית" lang="id" hreflang="id" data-title="Logaritma" data-language-autonym="Bahasa Indonesia" data-language-local-name="אינדונזית" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Logaritmo" title="Logaritmo – אידו" lang="io" hreflang="io" data-title="Logaritmo" data-language-autonym="Ido" data-language-local-name="אידו" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Logri" title="Logri – איסלנדית" lang="is" hreflang="is" data-title="Logri" data-language-autonym="Íslenska" data-language-local-name="איסלנדית" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Logaritmo" title="Logaritmo – איטלקית" lang="it" hreflang="it" data-title="Logaritmo" data-language-autonym="Italiano" data-language-local-name="איטלקית" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%AF%BE%E6%95%B0" title="対数 – יפנית" lang="ja" hreflang="ja" data-title="対数" data-language-autonym="日本語" data-language-local-name="יפנית" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Lagaridim" title="Lagaridim – ג׳מייקנית" lang="jam" hreflang="jam" data-title="Lagaridim" data-language-autonym="Patois" data-language-local-name="ג׳מייקנית" class="interlanguage-link-target"><span>Patois</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%9A%E1%83%9D%E1%83%92%E1%83%90%E1%83%A0%E1%83%98%E1%83%97%E1%83%9B%E1%83%98" title="ლოგარითმი – גאורגית" lang="ka" hreflang="ka" data-title="ლოგარითმი" data-language-autonym="ქართული" data-language-local-name="גאורגית" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9B%D0%BE%D0%B3%D0%B0%D1%80%D0%B8%D1%84%D0%BC" title="Логарифм – קזחית" lang="kk" hreflang="kk" data-title="Логарифм" data-language-autonym="Қазақша" data-language-local-name="קזחית" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%A1%9C%EA%B7%B8_(%EC%88%98%ED%95%99)" title="로그 (수학) – קוריאנית" lang="ko" hreflang="ko" data-title="로그 (수학)" data-language-autonym="한국어" data-language-local-name="קוריאנית" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Logarithmus" title="Logarithmus – לטינית" lang="la" hreflang="la" data-title="Logarithmus" data-language-autonym="Latina" data-language-local-name="לטינית" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lfn mw-list-item"><a href="https://lfn.wikipedia.org/wiki/Logaritmo" title="Logaritmo – לינגווה פראנקה נובה" lang="lfn" hreflang="lfn" data-title="Logaritmo" data-language-autonym="Lingua Franca Nova" data-language-local-name="לינגווה פראנקה נובה" class="interlanguage-link-target"><span>Lingua Franca Nova</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Logaritm" title="Logaritm – לומברדית" lang="lmo" hreflang="lmo" data-title="Logaritm" data-language-autonym="Lombard" data-language-local-name="לומברדית" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Logaritmas" title="Logaritmas – ליטאית" lang="lt" hreflang="lt" data-title="Logaritmas" data-language-autonym="Lietuvių" data-language-local-name="ליטאית" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Logaritms" title="Logaritms – לטבית" lang="lv" hreflang="lv" data-title="Logaritms" data-language-autonym="Latviešu" data-language-local-name="לטבית" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Anisa" title="Anisa – מלגשית" lang="mg" hreflang="mg" data-title="Anisa" data-language-autonym="Malagasy" data-language-local-name="מלגשית" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-mk badge-Q17437796 badge-featuredarticle mw-list-item" title="ערך מומלץ"><a href="https://mk.wikipedia.org/wiki/%D0%9B%D0%BE%D0%B3%D0%B0%D1%80%D0%B8%D1%82%D0%B0%D0%BC" title="Логаритам – מקדונית" lang="mk" hreflang="mk" data-title="Логаритам" data-language-autonym="Македонски" data-language-local-name="מקדונית" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%B2%E0%B5%8B%E0%B4%97%E0%B4%B0%E0%B4%BF%E0%B4%A4%E0%B4%82" title="ലോഗരിതം – מליאלאם" lang="ml" hreflang="ml" data-title="ലോഗരിതം" data-language-autonym="മലയാളം" data-language-local-name="מליאלאם" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%B2%E0%A5%89%E0%A4%97%E0%A5%85%E0%A4%B0%E0%A4%BF%E0%A4%A6%E0%A4%AE" title="लॉगॅरिदम – מראטהית" lang="mr" hreflang="mr" data-title="लॉगॅरिदम" data-language-autonym="मराठी" data-language-local-name="מראטהית" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Logaritma" title="Logaritma – מלאית" lang="ms" hreflang="ms" data-title="Logaritma" data-language-autonym="Bahasa Melayu" data-language-local-name="מלאית" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%9C%E1%80%B1%E1%80%AC%E1%80%B7%E1%80%82%E1%80%9B%E1%80%85%E1%80%BA%E1%80%9E%E1%80%99%E1%80%BA" title="လော့ဂရစ်သမ် – בורמזית" lang="my" hreflang="my" data-title="လော့ဂရစ်သမ်" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="בורמזית" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Logarithmus" title="Logarithmus – גרמנית תחתית" lang="nds" hreflang="nds" data-title="Logarithmus" data-language-autonym="Plattdüütsch" data-language-local-name="גרמנית תחתית" class="interlanguage-link-target"><span>Plattdüütsch</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Logaritme" title="Logaritme – הולנדית" lang="nl" hreflang="nl" data-title="Logaritme" data-language-autonym="Nederlands" data-language-local-name="הולנדית" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Logaritme" title="Logaritme – נורווגית חדשה" lang="nn" hreflang="nn" data-title="Logaritme" data-language-autonym="Norsk nynorsk" data-language-local-name="נורווגית חדשה" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Logaritme" title="Logaritme – נורווגית ספרותית" lang="nb" hreflang="nb" data-title="Logaritme" data-language-autonym="Norsk bokmål" data-language-local-name="נורווגית ספרותית" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Logaritme" title="Logaritme – אוקסיטנית" lang="oc" hreflang="oc" data-title="Logaritme" data-language-autonym="Occitan" data-language-local-name="אוקסיטנית" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Loogarizimii" title="Loogarizimii – אורומו" lang="om" hreflang="om" data-title="Loogarizimii" data-language-autonym="Oromoo" data-language-local-name="אורומו" class="interlanguage-link-target"><span>Oromoo</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%B2%E0%A8%98%E0%A9%82%E0%A8%97%E0%A8%A3%E0%A8%95" title="ਲਘੂਗਣਕ – פנג׳אבי" lang="pa" hreflang="pa" data-title="ਲਘੂਗਣਕ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="פנג׳אבי" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Logarytm" title="Logarytm – פולנית" lang="pl" hreflang="pl" data-title="Logarytm" data-language-autonym="Polski" data-language-local-name="פולנית" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D9%84%D8%A7%DA%AF%D8%B1%D8%AA%DA%BE%D9%85" title="لاگرتھم – פנג׳בית מערבית" lang="pnb" hreflang="pnb" data-title="لاگرتھم" data-language-autonym="پنجابی" data-language-local-name="פנג׳בית מערבית" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-pt badge-Q17437796 badge-featuredarticle mw-list-item" title="ערך מומלץ"><a href="https://pt.wikipedia.org/wiki/Logaritmo" title="Logaritmo – פורטוגזית" lang="pt" hreflang="pt" data-title="Logaritmo" data-language-autonym="Português" data-language-local-name="פורטוגזית" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Logaritm" title="Logaritm – רומנית" lang="ro" hreflang="ro" data-title="Logaritm" data-language-autonym="Română" data-language-local-name="רומנית" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru badge-Q17437796 badge-featuredarticle mw-list-item" title="ערך מומלץ"><a href="https://ru.wikipedia.org/wiki/%D0%9B%D0%BE%D0%B3%D0%B0%D1%80%D0%B8%D1%84%D0%BC" title="Логарифм – רוסית" lang="ru" hreflang="ru" data-title="Логарифм" data-language-autonym="Русский" data-language-local-name="רוסית" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sah mw-list-item"><a href="https://sah.wikipedia.org/wiki/%D0%9B%D0%BE%D0%B3%D0%B0%D1%80%D0%B8%D1%84%D0%BC" title="Логарифм – סאחה" lang="sah" hreflang="sah" data-title="Логарифм" data-language-autonym="Саха тыла" data-language-local-name="סאחה" class="interlanguage-link-target"><span>Саха тыла</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Logaritmu" title="Logaritmu – סיציליאנית" lang="scn" hreflang="scn" data-title="Logaritmu" data-language-autonym="Sicilianu" data-language-local-name="סיציליאנית" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sh badge-Q70893996 mw-list-item" title=""><a href="https://sh.wikipedia.org/wiki/%D0%9B%D0%BE%D0%B3%D0%B0%D1%80%D0%B8%D1%82%D0%B0%D0%BC" title="Логаритам – סרבו-קרואטית" lang="sh" hreflang="sh" data-title="Логаритам" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="סרבו-קרואטית" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%BD%E0%B6%9D%E0%B7%94_%E0%B6%9C%E0%B6%AB%E0%B6%9A" title="ලඝු ගණක – סינהלה" lang="si" hreflang="si" data-title="ලඝු ගණක" data-language-autonym="සිංහල" data-language-local-name="סינהלה" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Logarithm" title="Logarithm – אנגלית פשוטה" lang="en-simple" hreflang="en-simple" data-title="Logarithm" data-language-autonym="Simple English" data-language-local-name="אנגלית פשוטה" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Logaritmus" title="Logaritmus – סלובקית" lang="sk" hreflang="sk" data-title="Logaritmus" data-language-autonym="Slovenčina" data-language-local-name="סלובקית" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Logaritem" title="Logaritem – סלובנית" lang="sl" hreflang="sl" data-title="Logaritem" data-language-autonym="Slovenščina" data-language-local-name="סלובנית" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sn mw-list-item"><a href="https://sn.wikipedia.org/wiki/Daraunene" title="Daraunene – שונה" lang="sn" hreflang="sn" data-title="Daraunene" data-language-autonym="ChiShona" data-language-local-name="שונה" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Logaritmet" title="Logaritmet – אלבנית" lang="sq" hreflang="sq" data-title="Logaritmet" data-language-autonym="Shqip" data-language-local-name="אלבנית" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9B%D0%BE%D0%B3%D0%B0%D1%80%D0%B8%D1%82%D0%B0%D0%BC" title="Логаритам – סרבית" lang="sr" hreflang="sr" data-title="Логаритам" data-language-autonym="Српски / srpski" data-language-local-name="סרבית" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Logaritm" title="Logaritm – שוודית" lang="sv" hreflang="sv" data-title="Logaritm" data-language-autonym="Svenska" data-language-local-name="שוודית" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Logi" title="Logi – סווהילי" lang="sw" hreflang="sw" data-title="Logi" data-language-autonym="Kiswahili" data-language-local-name="סווהילי" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%AE%E0%AE%9F%E0%AE%95%E0%AF%8D%E0%AE%95%E0%AF%88" title="மடக்கை – טמילית" lang="ta" hreflang="ta" data-title="மடக்கை" data-language-autonym="தமிழ்" data-language-local-name="טמילית" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%A5%E0%B8%AD%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B8%B4%E0%B8%97%E0%B8%B6%E0%B8%A1" title="ลอการิทึม – תאית" lang="th" hreflang="th" data-title="ลอการิทึม" data-language-autonym="ไทย" data-language-local-name="תאית" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Logaritmo" title="Logaritmo – טאגאלוג" lang="tl" hreflang="tl" data-title="Logaritmo" data-language-autonym="Tagalog" data-language-local-name="טאגאלוג" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Logaritma" title="Logaritma – טורקית" lang="tr" hreflang="tr" data-title="Logaritma" data-language-autonym="Türkçe" data-language-local-name="טורקית" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%9B%D0%BE%D0%B3%D0%B0%D1%80%D0%B8%D1%84%D0%BC" title="Логарифм – טטרית" lang="tt" hreflang="tt" data-title="Логарифм" data-language-autonym="Татарча / tatarça" data-language-local-name="טטרית" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9B%D0%BE%D0%B3%D0%B0%D1%80%D0%B8%D1%84%D0%BC" title="Логарифм – אוקראינית" lang="uk" hreflang="uk" data-title="Логарифм" data-language-autonym="Українська" data-language-local-name="אוקראינית" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D9%84%D8%A7%DA%AF%D8%B1%D8%AA%DA%BE%D9%85" title="لاگرتھم – אורדו" lang="ur" hreflang="ur" data-title="لاگرتھم" data-language-autonym="اردو" data-language-local-name="אורדו" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Logarifm" title="Logarifm – אוזבקית" lang="uz" hreflang="uz" data-title="Logarifm" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="אוזבקית" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi badge-Q17437796 badge-featuredarticle mw-list-item" title="ערך מומלץ"><a href="https://vi.wikipedia.org/wiki/Logarit" title="Logarit – וייטנאמית" lang="vi" hreflang="vi" data-title="Logarit" data-language-autonym="Tiếng Việt" data-language-local-name="וייטנאמית" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Logaritmo" title="Logaritmo – וראית" lang="war" hreflang="war" data-title="Logaritmo" data-language-autonym="Winaray" data-language-local-name="וראית" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E5%AF%B9%E6%95%B0" title="对数 – סינית וו" lang="wuu" hreflang="wuu" data-title="对数" data-language-autonym="吴语" data-language-local-name="סינית וו" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%9C%D7%90%D7%92%D7%90%D7%A8%D7%99%D7%98%D7%9D" title="לאגאריטם – יידיש" lang="yi" hreflang="yi" data-title="לאגאריטם" data-language-autonym="ייִדיש" data-language-local-name="יידיש" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%AF%B9%E6%95%B0" title="对数 – סינית" lang="zh" hreflang="zh" data-title="对数" data-language-autonym="中文" data-language-local-name="סינית" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/T%C3%B9i-s%C3%B2%CD%98" title="Tùi-sò͘ – מין נאנית" lang="nan" hreflang="nan" data-title="Tùi-sò͘" 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href="/w/index.php?title=%D7%9E%D7%99%D7%95%D7%97%D7%93:%D7%A1%D7%A4%D7%A8&bookcmd=book_creator&referer=%D7%9C%D7%95%D7%92%D7%A8%D7%99%D7%AA%D7%9D"><span>יצירת ספר</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=%D7%9E%D7%99%D7%95%D7%97%D7%93:DownloadAsPdf&page=%D7%9C%D7%95%D7%92%D7%A8%D7%99%D7%AA%D7%9D&action=show-download-screen"><span>הורדה כ־PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=%D7%9C%D7%95%D7%92%D7%A8%D7%99%D7%AA%D7%9D&printable=yes" title="גרסה להדפסה של הדף הזה [p]" accesskey="p"><span>גרסה להדפסה</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> במיזמים אחרים </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Logarithm" hreflang="en"><span>ויקישיתוף</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q11197" title="קישור לפריט המשויך במאגר הנתונים [g]" accesskey="g"><span>פריט ויקינתונים</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="כלי דף"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="מראה"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">מראה</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">העברה לסרגל הצד</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">הסתרה</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">מתוך ויקיפדיה, האנציקלופדיה החופשית</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-rtl mw-parser-output" lang="he" dir="rtl"><table cellpadding="1" style="float: left; clear:both; border: 1px solid #8888aa; background: #f7f8ff; padding: 5px; font-size: 95%; margin: 0.5em 1em 0.5em 0.5em;"> <tbody><tr> <td style="text-align: center;"><span typeof="mw:File"><a href="/wiki/%D7%A1%D7%99%D7%9E%D7%95%D7%9F_%D7%9E%D7%AA%D7%9E%D7%98%D7%99" title="סימון מתמטי"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/60px-Nuvola_apps_edu_mathematics_blue-p.svg.png" decoding="async" width="60" height="60" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/90px-Nuvola_apps_edu_mathematics_blue-p.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/120px-Nuvola_apps_edu_mathematics_blue-p.svg.png 2x" data-file-width="128" data-file-height="128" /></a></span> <p>בערך זה<br />נעשה שימוש<br />בסימנים מוסכמים<br />מתחום המתמטיקה.<br />להבהרת הסימנים<br />ראו <a href="/wiki/%D7%A1%D7%99%D7%9E%D7%95%D7%9F_%D7%9E%D7%AA%D7%9E%D7%98%D7%99" title="סימון מתמטי">סימון מתמטי</a>. </p> </td></tr></tbody></table> <figure typeof="mw:File/Thumb"><a href="/wiki/%D7%A7%D7%95%D7%91%D7%A5:Log.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Log.png/250px-Log.png" decoding="async" width="250" height="226" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Log.png/375px-Log.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Log.png/500px-Log.png 2x" data-file-width="650" data-file-height="587" /></a><figcaption>לוגריתמים בבסיסים שונים: <span style="color:red;"><a href="/wiki/%D7%90%D7%93%D7%95%D7%9D" title="אדום">אדום</a></span> הוא בבסיס <a href="/wiki/E_(%D7%A7%D7%91%D7%95%D7%A2_%D7%9E%D7%AA%D7%9E%D7%98%D7%99)" title="E (קבוע מתמטי)">e</a>, <span style="color:yellow;"><a href="/wiki/%D7%A6%D7%94%D7%95%D7%91" title="צהוב">צהוב</a></span> בבסיס 2, <span style="color:blue;"><a href="/wiki/%D7%9B%D7%97%D7%95%D7%9C" title="כחול">כחול</a></span> בבסיס 1/2. לוגריתמים בכל הבסיסים עוברים דרך הנקודה (1,0), שכן כל מספר ב<a href="/wiki/%D7%97%D7%96%D7%A7%D7%94_(%D7%9E%D7%AA%D7%9E%D7%98%D7%99%D7%A7%D7%94)" title="חזקה (מתמטיקה)">חזקת</a> <a href="/wiki/0_(%D7%9E%D7%A1%D7%A4%D7%A8)" title="0 (מספר)">0</a> הוא <a href="/wiki/1_(%D7%9E%D7%A1%D7%A4%D7%A8)" title="1 (מספר)">1</a>.</figcaption></figure> <p><b>לוגריתם</b> (Logarithm) הוא <a href="/wiki/%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%94_%D7%94%D7%A4%D7%95%D7%9B%D7%94" class="mw-redirect" title="פונקציה הפוכה">פונקציה הפוכה</a> ל<a href="/wiki/%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%94_%D7%9E%D7%A2%D7%A8%D7%99%D7%9B%D7%99%D7%AA" title="פונקציה מעריכית">פונקציה המעריכית</a>. הפונקציה <a href="/wiki/%D7%A1%D7%99%D7%9E%D7%95%D7%9F_%D7%9E%D7%AA%D7%9E%D7%98%D7%99" title="סימון מתמטי">מסומנת</a> באותיות <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \log }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>log</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \log }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/79e4debd0ab1c6ce342d0172a7643733305c37bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.972ex; height:2.509ex;" alt="{\displaystyle \log }"></span>. פעולה זו מוצאת את ה<a href="/wiki/%D7%9E%D7%A2%D7%A8%D7%99%D7%9A" class="mw-redirect" title="מעריך">מעריך</a> בהינתן בסיס ותוצאה, כלומר היא עונה על השאלה: "באיזו <a href="/wiki/%D7%97%D7%96%D7%A7%D7%94_(%D7%9E%D7%AA%D7%9E%D7%98%D7%99%D7%A7%D7%94)" title="חזקה (מתמטיקה)">חזקה</a> יש להעלות את הבסיס b כדי לקבל את התוצאה a?". לוגריתם של a לפי בסיס b נכתב <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \log _{b}a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mo>⁡</mo> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \log _{b}a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/19448f02c7456ab7585d9466920f67dab9343d97" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.526ex; height:2.676ex;" alt="{\displaystyle \log _{b}a}"></span>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="הגדרה"><span id=".D7.94.D7.92.D7.93.D7.A8.D7.94"></span>הגדרה</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D7%9C%D7%95%D7%92%D7%A8%D7%99%D7%AA%D7%9D&action=edit&section=1" title="עריכת קוד המקור של הפרק: הגדרה"><span>עריכת קוד מקור</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D7%9C%D7%95%D7%92%D7%A8%D7%99%D7%AA%D7%9D&veaction=edit&section=1" title="עריכת פסקה: "הגדרה"" class="mw-editsection-visualeditor"><span>עריכה</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>כאמור, הלוגריתם של <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}"></span> ב<b>בסיס</b> נתון <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/32a4603b6617346e905e275ffc3ebe9b61296a2a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.578ex; height:2.176ex;" alt="{\displaystyle \ b}"></span> (הגדול מאפס ושונה מ-1 ובהתאם x חיובי), הוא ה<a href="/wiki/%D7%97%D7%96%D7%A7%D7%94_(%D7%9E%D7%AA%D7%9E%D7%98%D7%99%D7%A7%D7%94)" title="חזקה (מתמטיקה)">חזקה</a> שבה יש להעלות את <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/32a4603b6617346e905e275ffc3ebe9b61296a2a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.578ex; height:2.176ex;" alt="{\displaystyle \ b}"></span> כדי לקבל את <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9923068b5684340554217dfc8b2b968523527d9a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.91ex; height:1.676ex;" alt="{\displaystyle \ x}"></span>.<br />אם <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ b>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>b</mi> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ b>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d33e0264aecbc089dd90c64414a04fe1d1cef836" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.839ex; height:2.176ex;" alt="{\displaystyle \ b>0}"></span> וגם <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ b^{y}=x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msup> <mo>=</mo> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ b^{y}=x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/63585feba1182dffef6f359c0050df4ef381bca1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.056ex; height:2.343ex;" alt="{\displaystyle \ b^{y}=x}"></span>, נאמר ש־<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e64598c4f945fe21fbf547a5d349969c7e6d852d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.736ex; height:2.009ex;" alt="{\displaystyle \ y}"></span> הוא לוגריתם של <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9923068b5684340554217dfc8b2b968523527d9a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.91ex; height:1.676ex;" alt="{\displaystyle \ x}"></span> לפי בסיס <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/32a4603b6617346e905e275ffc3ebe9b61296a2a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.578ex; height:2.176ex;" alt="{\displaystyle \ b}"></span>, ונכתוב זאת: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ y=\log _{b}x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>y</mi> <mo>=</mo> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mo>⁡</mo> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ y=\log _{b}x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/38bccdd687b30b0c91b75fb76bb49d6f12ef845c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.461ex; height:2.676ex;" alt="{\displaystyle \ y=\log _{b}x}"></span>. </p><p>כך, הזהות הלוגריתמית היסודית היא: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ b^{log_{b}x}=x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> <mi>o</mi> <msub> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mi>x</mi> </mrow> </msup> <mo>=</mo> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ b^{log_{b}x}=x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f198a05bf478736d74c8842de01c05d3a6c45b93" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:9.988ex; height:2.676ex;" alt="{\displaystyle \ b^{log_{b}x}=x}"></span>. </p> <dl><dd>דוגמה: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ \log _{10}100=2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mo>⁡</mo> <mn>100</mn> <mo>=</mo> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ \log _{10}100=2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/00686a7af7a7f112e222179661da2ad3e4bceb18" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.951ex; height:2.676ex;" alt="{\displaystyle \ \log _{10}100=2}"></span>, משום ש- <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ 100=10^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mn>100</mn> <mo>=</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ 100=10^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6700151576ee3e35b2990edce44126ee0945c3aa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:10.546ex; height:2.676ex;" alt="{\displaystyle \ 100=10^{2}}"></span>.</dd> <dd>ובמילים: הלוגריתם של <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ 100}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mn>100</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ 100}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4dc83c0950015f43ecb8f11d9231cc9a8ab48544" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.068ex; height:2.176ex;" alt="{\displaystyle \ 100}"></span> לפי בסיס <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ 10}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mn>10</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ 10}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2d616480b76bc4e8a1bbd7de00eb4920d121734b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.906ex; height:2.176ex;" alt="{\displaystyle \ 10}"></span> הוא <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ 2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ 2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6cba752020bb6098235c4f7b8751ad0be05c5b35" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle \ 2}"></span>, משום ש־<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ 10}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mn>10</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ 10}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2d616480b76bc4e8a1bbd7de00eb4920d121734b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.906ex; height:2.176ex;" alt="{\displaystyle \ 10}"></span> בחזקת <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ 2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ 2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6cba752020bb6098235c4f7b8751ad0be05c5b35" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle \ 2}"></span> שווה ל־<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ 100}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mn>100</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ 100}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4dc83c0950015f43ecb8f11d9231cc9a8ab48544" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.068ex; height:2.176ex;" alt="{\displaystyle \ 100}"></span>.</dd></dl> <p><b>בסיס ברירת המחדל:</b> </p><p>שימוש בסימון <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ \log }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>log</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ \log }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/60c20bcb560a122e2faca1fa34a979566a804319" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.939ex; height:2.509ex;" alt="{\displaystyle \ \log }"></span> ללא ציון הבסיס עלול לבלבל מעט, משום שמשמעותו משתנה לפי ההקשר: </p> <ul><li>בטקסטים מתמטיים משמעותו <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ \log _{e}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ \log _{e}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a435c7ff046eedc57ff4f3531946b41264a112da" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.938ex; height:2.676ex;" alt="{\displaystyle \ \log _{e}}"></span> (ה<a href="/wiki/%D7%9C%D7%95%D7%92%D7%A8%D7%99%D7%AA%D7%9D_%D7%98%D7%91%D7%A2%D7%99" title="לוגריתם טבעי">לוגריתם הטבעי</a>, שבסיסו <a href="/wiki/E_(%D7%A7%D7%91%D7%95%D7%A2_%D7%9E%D7%AA%D7%9E%D7%98%D7%99)" title="E (קבוע מתמטי)">מספר אוילר</a>). נהוג לכתוב פונקציה זו בקיצור <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ \ln }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>ln</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ \ln }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/30f1ed5136dcaaa358cf290230e2dd544e30bc83" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.907ex; height:2.176ex;" alt="{\displaystyle \ \ln }"></span>.</li> <li>בטקסטים <a href="/wiki/%D7%94%D7%A0%D7%93%D7%A1%D7%94" title="הנדסה">הנדסיים</a> משמעותו <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ \log _{10}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ \log _{10}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7b3f826d88ae54441c5585c4512a2eab308b5e88" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.816ex; height:2.676ex;" alt="{\displaystyle \ \log _{10}}"></span>, לעיתים נכתב בקיצור <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ {\mbox{lg}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>lg</mtext> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ {\mbox{lg}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0b92fce29a1848987d95ea483b327e3238ac4212" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.39ex; height:2.509ex;" alt="{\displaystyle \ {\mbox{lg}}}"></span>.</li> <li>בטקסטים שעוסקים ב<a href="/wiki/%D7%9E%D7%93%D7%A2%D7%99_%D7%94%D7%9E%D7%97%D7%A9%D7%91" title="מדעי המחשב">מדעי המחשב</a> משמעותו <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ \log _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ \log _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c08d3c0ee3b649ee1b2aa680ef1c90d79586b9e8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.994ex; height:2.676ex;" alt="{\displaystyle \ \log _{2}}"></span>, לעיתים נכתב בקיצור <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ {\mbox{lb}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>lb</mtext> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ {\mbox{lb}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/46058185c79db96abc96e86e1a8959b1fb79f4c8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.52ex; height:2.176ex;" alt="{\displaystyle \ {\mbox{lb}}}"></span>.</li></ul> <div class="mw-heading mw-heading2"><h2 id="רקע_היסטורי"><span id=".D7.A8.D7.A7.D7.A2_.D7.94.D7.99.D7.A1.D7.98.D7.95.D7.A8.D7.99"></span>רקע היסטורי</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D7%9C%D7%95%D7%92%D7%A8%D7%99%D7%AA%D7%9D&action=edit&section=2" title="עריכת קוד המקור של הפרק: רקע היסטורי"><span>עריכת קוד מקור</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D7%9C%D7%95%D7%92%D7%A8%D7%99%D7%AA%D7%9D&veaction=edit&section=2" title="עריכת פסקה: "רקע היסטורי"" class="mw-editsection-visualeditor"><span>עריכה</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>הלוגריתמים הוכנסו לשימוש בתחילת <a href="/wiki/%D7%94%D7%9E%D7%90%D7%94_%D7%94-17" title="המאה ה-17">המאה ה-17</a> על ידי <a href="/wiki/%D7%92%27%D7%95%D7%9F_%D7%A0%D7%A4%D7%99%D7%99%D7%A8" title="ג'ון נפייר">ג'ון נפייר</a> <a href="/wiki/%D7%9C%D7%95%D7%97_%D7%94%D7%9C%D7%95%D7%92%D7%A8%D7%99%D7%AA%D7%9E%D7%99%D7%9D_%D7%A9%D7%9C_%D7%A0%D7%90%D7%A4%D7%99%D7%99%D7%A8" title="לוח הלוגריתמים של נאפייר">בספריו</a>. עד להחלפתם על ידי ה<a href="/wiki/%D7%9E%D7%97%D7%A9%D7%91" title="מחשב">מחשב</a> וה<a href="/wiki/%D7%9E%D7%97%D7%A9%D7%91%D7%95%D7%9F" title="מחשבון">מחשבון</a>, בחצי השני של <a href="/wiki/%D7%94%D7%9E%D7%90%D7%94_%D7%94-20" title="המאה ה-20">המאה ה-20</a>, היו הלוגריתמים כלי עזר עיקרי ל<a href="/wiki/%D7%97%D7%99%D7%A9%D7%95%D7%91" title="חישוב">חישוב</a>, באמצעות <a href="/wiki/%D7%9C%D7%95%D7%97_%D7%9C%D7%95%D7%92%D7%A8%D7%99%D7%AA%D7%9E%D7%99%D7%9D" title="לוח לוגריתמים">לוח לוגריתמים</a> ובאמצעות <a href="/wiki/%D7%A1%D7%A8%D7%92%D7%9C_%D7%97%D7%99%D7%A9%D7%95%D7%91" title="סרגל חישוב">סרגל חישוב</a>. הרעיון הבסיסי מאחורי שני עזרי חישוב אלה הוא הכלל לפיו לוגריתם של מכפלה שווה לסכום הלוגריתמים של כל אחד מאיברי המכפלה. כלל זה מאפשר להחליף פעולת <a href="/wiki/%D7%9B%D7%A4%D7%9C" title="כפל">כפל</a>, שהיא פעולה מורכבת יחסית, בפעולת החיבור הפשוטה יותר. בכלים אלה נעשה שימוש בלוגריתמים לפי בסיס <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ 10}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mn>10</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ 10}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2d616480b76bc4e8a1bbd7de00eb4920d121734b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.906ex; height:2.176ex;" alt="{\displaystyle \ 10}"></span>. </p> <div class="mw-heading mw-heading2"><h2 id="חוקי_הלוגריתמים"><span id=".D7.97.D7.95.D7.A7.D7.99_.D7.94.D7.9C.D7.95.D7.92.D7.A8.D7.99.D7.AA.D7.9E.D7.99.D7.9D"></span>חוקי הלוגריתמים</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D7%9C%D7%95%D7%92%D7%A8%D7%99%D7%AA%D7%9D&action=edit&section=3" title="עריכת קוד המקור של הפרק: חוקי הלוגריתמים"><span>עריכת קוד מקור</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D7%9C%D7%95%D7%92%D7%A8%D7%99%D7%AA%D7%9D&veaction=edit&section=3" title="עריכת פסקה: "חוקי הלוגריתמים"" class="mw-editsection-visualeditor"><span>עריכה</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>החוקים המפורטים להלן נכונים לכל <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ a,b,c,d}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo>,</mo> <mi>c</mi> <mo>,</mo> <mi>d</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ a,b,c,d}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d3af59d50cd21d42c97ea724bb7fdf6fcdfe9cf9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.133ex; height:2.509ex;" alt="{\displaystyle \ a,b,c,d}"></span> <a href="/wiki/%D7%9E%D7%A1%D7%A4%D7%A8_%D7%9E%D7%9E%D7%A9%D7%99" title="מספר ממשי">ממשיים</a> חיוביים, ובתנאי שבסיס הלוגריתמים שונה מ־1. </p> <table border="1" width="95%" align="right" cellpadding="8" cellspacing="1"> <tbody><tr> <td valign="top" bgcolor="#F0F0F0" width="50%"><b>ערכים מיוחדים</b> </td> <td dir="LTR"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ \log _{a}(1)=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> <mo>⁡</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ \log _{a}(1)=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a16813e05c3fc9fc232456ae98576c57cd59644b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.274ex; height:2.843ex;" alt="{\displaystyle \ \log _{a}(1)=0}"></span> <br /> <br /> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ \log _{a}(a)=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ \log _{a}(a)=1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/808899835e63e048f9a32f8c395f93fb61e185b1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.341ex; height:2.843ex;" alt="{\displaystyle \ \log _{a}(a)=1}"></span> </p> </td></tr> <tr> <td valign="top" bgcolor="#F0F0F0"><b>כפל, חילוק והעלאה בחזקה</b> <p>חוקים אלו יכולים להקל על חישובי כפל, חילוק, חזקה ושורש, באמצעות לוח לוגריתמים או סרגל חישוב. </p> </td> <td dir="LTR"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ \log _{c}(a\cdot b)=\log _{c}(a)+\log _{c}(b)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo>⋅</mo> <mi>b</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo stretchy="false">)</mo> <mo>+</mo> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>b</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ \log _{c}(a\cdot b)=\log _{c}(a)+\log _{c}(b)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/db46a532cda788998bfdc98ed72d43e594a4db73" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:30.216ex; height:2.843ex;" alt="{\displaystyle \ \log _{c}(a\cdot b)=\log _{c}(a)+\log _{c}(b)}"></span> <br /> <br /> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ \log _{c}\left({\frac {a}{b}}\right)=\log _{c}(a)-\log _{c}(b)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>a</mi> <mi>b</mi> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo stretchy="false">)</mo> <mo>−</mo> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>b</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ \log _{c}\left({\frac {a}{b}}\right)=\log _{c}(a)-\log _{c}(b)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c2d51b52be398f423a5d7b82c0440d73c7563566" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:29.342ex; height:5.009ex;" alt="{\displaystyle \ \log _{c}\left({\frac {a}{b}}\right)=\log _{c}(a)-\log _{c}(b)}"></span> <br /> <br /> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ {\log _{a}b}\cdot {\log _{c}d}={\log _{c}b}\cdot {\log _{a}d}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> <mo>⁡</mo> <mi>b</mi> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mo>⁡</mo> <mi>d</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mo>⁡</mo> <mi>b</mi> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> <mo>⁡</mo> <mi>d</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ {\log _{a}b}\cdot {\log _{c}d}={\log _{c}b}\cdot {\log _{a}d}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c9333f954fb81ceaccadd06f62071e3a9232ec42" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:28.992ex; height:2.676ex;" alt="{\displaystyle \ {\log _{a}b}\cdot {\log _{c}d}={\log _{c}b}\cdot {\log _{a}d}}"></span> <br /> </p> <div dir="RTL">לכל <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6d3eac7d19d1a7a70c7815839b49b031fc7076e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.629ex; height:1.676ex;" alt="{\displaystyle \ r}"></span> <a href="/wiki/%D7%9E%D7%A1%D7%A4%D7%A8_%D7%9E%D7%9E%D7%A9%D7%99" title="מספר ממשי">ממשי</a>:</div> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ \log _{c}(a^{r})=r\cdot \log _{c}(a)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mo>⁡</mo> <mo stretchy="false">(</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msup> <mo stretchy="false">)</mo> <mo>=</mo> <mi>r</mi> <mo>⋅</mo> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ \log _{c}(a^{r})=r\cdot \log _{c}(a)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/97ac15f555926a717047c228a8c1321d232563ce" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:21.678ex; height:2.843ex;" alt="{\displaystyle \ \log _{c}(a^{r})=r\cdot \log _{c}(a)}"></span> </p> </td></tr> <tr> <td valign="top" bgcolor="#F0F0F0"><b>הלוגריתם והפונקציה המעריכית</b> <p>חוקים אלו שימושיים לפתרון משוואות בהן הנעלם הוא "מעריך" של חזקה. </p> </td> <td dir="LTR"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ x^{\log _{a}b}=b^{\log _{a}x}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> <mo>⁡</mo> <mi>b</mi> </mrow> </msup> <mo>=</mo> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> <mo>⁡</mo> <mi>x</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ x^{\log _{a}b}=b^{\log _{a}x}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5bbc417ad7b7761a2cf9918dfd8a43647ee2679a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:14.834ex; height:2.676ex;" alt="{\displaystyle \ x^{\log _{a}b}=b^{\log _{a}x}}"></span> <p><br /> <br /> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ a^{\log _{a}b}=b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> <mo>⁡</mo> <mi>b</mi> </mrow> </msup> <mo>=</mo> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ a^{\log _{a}b}=b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/362e7a44c5b9faae398c5d0656becb221a42291d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:10.203ex; height:2.676ex;" alt="{\displaystyle \ a^{\log _{a}b}=b}"></span> <br /> <br /> </p> <div dir="RTL">לכל <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6d3eac7d19d1a7a70c7815839b49b031fc7076e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.629ex; height:1.676ex;" alt="{\displaystyle \ r}"></span> <a href="/wiki/%D7%9E%D7%A1%D7%A4%D7%A8_%D7%9E%D7%9E%D7%A9%D7%99" title="מספר ממשי">ממשי</a>:</div> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ \log _{a}a^{r}=r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> <mo>⁡</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msup> <mo>=</mo> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ \log _{a}a^{r}=r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e2ca1f565a0857161689b2db4401ef4f1c31be43" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.779ex; height:2.843ex;" alt="{\displaystyle \ \log _{a}a^{r}=r}"></span> </p> </td></tr> <tr> <td valign="top" bgcolor="#F0F0F0"><b>שינוי בסיס הלוגריתם</b> <p>חוק זה שימושי להמרת לוגריתמים במחשבונים. לרוב המחשבונים יש לחצנים לחישוב לוגריתם טבעי (ln) ולוגריתם בבסיס 10 (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ \log _{10}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ \log _{10}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7b3f826d88ae54441c5585c4512a2eab308b5e88" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.816ex; height:2.676ex;" alt="{\displaystyle \ \log _{10}}"></span>), אבל לא לבסיס 2 (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ \log _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ \log _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c08d3c0ee3b649ee1b2aa680ef1c90d79586b9e8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.994ex; height:2.676ex;" alt="{\displaystyle \ \log _{2}}"></span>). </p><p>כדי לחשב את <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ \log _{2}100}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>⁡</mo> <mn>100</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ \log _{2}100}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0fc0593957748a331ddb071aabe0e1ac5acdd786" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.868ex; height:2.676ex;" alt="{\displaystyle \ \log _{2}100}"></span>, מחשבים: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ {\frac {\log _{10}100}{\log _{10}2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mo>⁡</mo> <mn>100</mn> </mrow> <mrow> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mo>⁡</mo> <mn>2</mn> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ {\frac {\log _{10}100}{\log _{10}2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4f6add8f17597ec11abf7f9919eb8c7c361e80b7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:10.139ex; height:6.176ex;" alt="{\displaystyle \ {\frac {\log _{10}100}{\log _{10}2}}}"></span> או <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ {\frac {\ln {100}}{\ln {2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>ln</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>100</mn> </mrow> </mrow> <mrow> <mi>ln</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ {\frac {\ln {100}}{\ln {2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6304c80e04a77dbb30fd91f64f5ff676fc695ab7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:7.231ex; height:5.343ex;" alt="{\displaystyle \ {\frac {\ln {100}}{\ln {2}}}}"></span> שנותן תוצאה זהה. </p> </td> <td dir="LTR"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ \log _{a}b={\frac {\log _{c}b}{\log _{c}a}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> <mo>⁡</mo> <mi>b</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mo>⁡</mo> <mi>b</mi> </mrow> <mrow> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mo>⁡</mo> <mi>a</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ \log _{a}b={\frac {\log _{c}b}{\log _{c}a}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cc975e5fc9aa542473303d2ae3eb28aef9d1cc88" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:15.893ex; height:6.176ex;" alt="{\displaystyle \ \log _{a}b={\frac {\log _{c}b}{\log _{c}a}}}"></span> <br /> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ \log _{a}b={\frac {1}{\log _{b}a}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> <mo>⁡</mo> <mi>b</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mo>⁡</mo> <mi>a</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ \log _{a}b={\frac {1}{\log _{b}a}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e2f07e54039379d400a2d564c55945a730e8b585" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:15.887ex; height:5.843ex;" alt="{\displaystyle \ \log _{a}b={\frac {1}{\log _{b}a}}}"></span> </p> </td></tr> <tr> <td valign="top" bgcolor="#F0F0F0"><b><a href="/wiki/%D7%92%D7%91%D7%95%D7%9C_(%D7%9E%D7%AA%D7%9E%D7%98%D7%99%D7%A7%D7%94)" title="גבול (מתמטיקה)">גבולות</a></b> </td> <td dir="LTR"> <div dir="RTL">כאשר a > 1:</div> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ \lim _{x\to 0}\log _{a}(x)=-\infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> <mo stretchy="false">→</mo> <mn>0</mn> </mrow> </munder> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo>−</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ \lim _{x\to 0}\log _{a}(x)=-\infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/279f957afd7bc7a123009667ddaa27559b4732d4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:19.203ex; height:4.009ex;" alt="{\displaystyle \ \lim _{x\to 0}\log _{a}(x)=-\infty }"></span> </p> <div dir="RTL">כאשר a < 1:</div> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ \lim _{x\to 0}\log _{a}(x)=\infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> <mo stretchy="false">→</mo> <mn>0</mn> </mrow> </munder> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ \lim _{x\to 0}\log _{a}(x)=\infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3f99adb5505f558ac3bb5e9b803f94acb944bfe8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:17.395ex; height:4.009ex;" alt="{\displaystyle \ \lim _{x\to 0}\log _{a}(x)=\infty }"></span> </p> <div dir="RTL">כאשר a > 1:</div> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ \lim _{x\to \infty }\log _{a}(x)=\infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> <mo stretchy="false">→</mo> <mi mathvariant="normal">∞</mi> </mrow> </munder> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ \lim _{x\to \infty }\log _{a}(x)=\infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6c797e3e22806f59e6c2e64501219ffec0705fd2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:18.216ex; height:3.843ex;" alt="{\displaystyle \ \lim _{x\to \infty }\log _{a}(x)=\infty }"></span> </p> <div dir="RTL">כאשר a < 1:</div> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ \lim _{x\to \infty }\log _{a}(x)=-\infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> <mo stretchy="false">→</mo> <mi mathvariant="normal">∞</mi> </mrow> </munder> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo>−</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ \lim _{x\to \infty }\log _{a}(x)=-\infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e7e13446deba1566184aad703a04a586446a320f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:20.024ex; height:3.843ex;" alt="{\displaystyle \ \lim _{x\to \infty }\log _{a}(x)=-\infty }"></span> <br /> <br /> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ \lim _{x\to 0}\log _{a}(x)\cdot x^{b}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> <mo stretchy="false">→</mo> <mn>0</mn> </mrow> </munder> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msup> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ \lim _{x\to 0}\log _{a}(x)\cdot x^{b}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bb75d1c9241a37437cbe4e39f0b746833ee3bb19" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:20.18ex; height:4.343ex;" alt="{\displaystyle \ \lim _{x\to 0}\log _{a}(x)\cdot x^{b}=0}"></span> <br /> <br /> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ \lim _{x\to \infty }\log _{a}(x)/x^{b}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> <mo stretchy="false">→</mo> <mi mathvariant="normal">∞</mi> </mrow> </munder> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msup> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ \lim _{x\to \infty }\log _{a}(x)/x^{b}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/58ecce84f5ff5ee14f89d032b2416851b6da20a4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:20.485ex; height:4.176ex;" alt="{\displaystyle \ \lim _{x\to \infty }\log _{a}(x)/x^{b}=0}"></span> </p> </td></tr> <tr> <td valign="top" bgcolor="#F0F0F0"><b><a href="/wiki/%D7%A0%D7%92%D7%96%D7%A8%D7%AA" title="נגזרת">נגזרת</a></b> </td> <td dir="LTR"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ {d \over dx}\log _{a}(x)={\frac {1}{\ln(a)}}{1 \over x}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>d</mi> <mrow> <mi>d</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>ln</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>x</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ {d \over dx}\log _{a}(x)={\frac {1}{\ln(a)}}{1 \over x}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/98a3ad4230109b9a8c296f5beb5bc7a13ce6e356" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:22.641ex; height:6.176ex;" alt="{\displaystyle \ {d \over dx}\log _{a}(x)={\frac {1}{\ln(a)}}{1 \over x}}"></span> </p> </td></tr> <tr> <td valign="top" bgcolor="#F0F0F0"><b><a href="/wiki/%D7%90%D7%99%D7%A0%D7%98%D7%92%D7%A8%D7%9C" title="אינטגרל">אינטגרל</a></b> </td> <td dir="LTR"> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ \int \log _{a}(x)\,dx=x\log _{a}(x)-{\frac {x}{\ln(a)}}+C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mo>∫</mo> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mi>x</mi> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>x</mi> <mrow> <mi>ln</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mo>+</mo> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ \int \log _{a}(x)\,dx=x\log _{a}(x)-{\frac {x}{\ln(a)}}+C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/16e1655c9ed33379a263043862392114a4ae2d57" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:38.983ex; height:6.009ex;" alt="{\displaystyle \ \int \log _{a}(x)\,dx=x\log _{a}(x)-{\frac {x}{\ln(a)}}+C}"></span> </p> </td></tr></tbody></table> <div style="clear: both;"></div> <p><br /> </p> <div class="mw-heading mw-heading2"><h2 id="שיטות_לחישוב_לוגריתמים"><span id=".D7.A9.D7.99.D7.98.D7.95.D7.AA_.D7.9C.D7.97.D7.99.D7.A9.D7.95.D7.91_.D7.9C.D7.95.D7.92.D7.A8.D7.99.D7.AA.D7.9E.D7.99.D7.9D"></span>שיטות לחישוב לוגריתמים</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D7%9C%D7%95%D7%92%D7%A8%D7%99%D7%AA%D7%9D&action=edit&section=4" title="עריכת קוד המקור של הפרק: שיטות לחישוב לוגריתמים"><span>עריכת קוד מקור</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D7%9C%D7%95%D7%92%D7%A8%D7%99%D7%AA%D7%9D&veaction=edit&section=4" title="עריכת פסקה: "שיטות לחישוב לוגריתמים"" class="mw-editsection-visualeditor"><span>עריכה</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="האלגוריתם_של_פיינמן"><span id=".D7.94.D7.90.D7.9C.D7.92.D7.95.D7.A8.D7.99.D7.AA.D7.9D_.D7.A9.D7.9C_.D7.A4.D7.99.D7.99.D7.A0.D7.9E.D7.9F"></span>האלגוריתם של פיינמן</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D7%9C%D7%95%D7%92%D7%A8%D7%99%D7%AA%D7%9D&action=edit&section=5" title="עריכת קוד המקור של הפרק: האלגוריתם של פיינמן"><span>עריכת קוד מקור</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D7%9C%D7%95%D7%92%D7%A8%D7%99%D7%AA%D7%9D&veaction=edit&section=5" title="עריכת פסקה: "האלגוריתם של פיינמן"" class="mw-editsection-visualeditor"><span>עריכה</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/%D7%A8%D7%99%D7%A6%27%D7%A8%D7%93_%D7%A4%D7%99%D7%99%D7%A0%D7%9E%D7%9F" title="ריצ'רד פיינמן">ריצ'רד פיינמן</a> המציא <a href="/wiki/%D7%90%D7%9C%D7%92%D7%95%D7%A8%D7%99%D7%AA%D7%9D" title="אלגוריתם">אלגוריתם</a> המאפשר לחשב לוגריתמים בקלות יחסית באמצעות שימוש בתהליך שדומה מאוד לחילוק ארוך ובטבלת ערכים לוגריתמיים מוכנים, שהוא שימושי מאוד במכונות חישוב בינאריות. הרעיון של האלגוריתם מתבסס על העובדה שכל מספר ממשי בטווח בין 1 ל-2 ניתן לפירוק לגורמים מהצורה <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (1+2^{-k})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi>k</mi> </mrow> </msup> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (1+2^{-k})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/60e1398a87dd9bc63e42d4b60379070bf610a9f6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.342ex; height:3.176ex;" alt="{\displaystyle (1+2^{-k})}"></span> באופן יחיד. האלגוריתם בונה מכפלות <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4dc73bf40314945ff376bd363916a738548d40a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}"></span> באופן סדרתי: אם <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P\cdot (1+2^{-k})<x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mo>⋅</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi>k</mi> </mrow> </msup> <mo stretchy="false">)</mo> <mo><</mo> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P\cdot (1+2^{-k})<x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3dac162907c2a60228070f13220799a55a8f8913" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:17.195ex; height:3.176ex;" alt="{\displaystyle P\cdot (1+2^{-k})<x}"></span>, אז משנים את P ל-<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P^{*}=P\cdot (1+2^{-k})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> <mo>=</mo> <mi>P</mi> <mo>⋅</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi>k</mi> </mrow> </msup> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P^{*}=P\cdot (1+2^{-k})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81af86325361949bf6c99a8ce89848bcf7c1e1f4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.741ex; height:3.176ex;" alt="{\displaystyle P^{*}=P\cdot (1+2^{-k})}"></span>. לאחר מכן בוחנים אם הגורם הבא בפיתוח של המספר הממשי לפירוק לגורמים הוא מהצורה <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (1+2^{-(k+1)})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mo stretchy="false">(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msup> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (1+2^{-(k+1)})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/528b8ab1e3852fe6570bf84a4d0fc9bdd165e103" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.722ex; height:3.343ex;" alt="{\displaystyle (1+2^{-(k+1)})}"></span>. אם <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P^{*}\cdot (1+2^{-(k+1)})<x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> <mo>⋅</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mo stretchy="false">(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </msup> <mo stretchy="false">)</mo> <mo><</mo> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P^{*}\cdot (1+2^{-(k+1)})<x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/08a4606f9cc418fc24bba3b67263dc1085939f50" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:21.705ex; height:3.343ex;" alt="{\displaystyle P^{*}\cdot (1+2^{-(k+1)})<x}"></span> אז גילינו עוד גורם בפירוק של x לגורמים. האלגוריתם מפסיק כאשר k <a href="/wiki/%D7%92%D7%93%D7%95%D7%9C_%D7%9E%D7%A1%D7%A4%D7%99%D7%A7" title="גדול מספיק">גדול מספיק</a> כדי להשיג את הדיוק הדרוש. כיוון ש-<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \log(x)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>log</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \log(x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4157d3b51ac7b147fca145d431d58ec92abc1f70" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.111ex; height:2.843ex;" alt="{\displaystyle \log(x)}"></span> הוא סכום של איברים מהצורה <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \log(1+2^{-k})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>log</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi>k</mi> </mrow> </msup> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \log(1+2^{-k})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3c00b267866d2903ae41167c5e2f617a77fb015c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.314ex; height:3.176ex;" alt="{\displaystyle \log(1+2^{-k})}"></span> אשר הופיעו בפירוק לגורמים של x, אז <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \log(x)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>log</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \log(x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4157d3b51ac7b147fca145d431d58ec92abc1f70" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.111ex; height:2.843ex;" alt="{\displaystyle \log(x)}"></span> ניתן לחישוב בעזרת חיבור פשוט, בעזרת טבלת ערכים של <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \log(1+2^{-k})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>log</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi>k</mi> </mrow> </msup> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \log(1+2^{-k})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3c00b267866d2903ae41167c5e2f617a77fb015c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.314ex; height:3.176ex;" alt="{\displaystyle \log(1+2^{-k})}"></span> עבור כל ערכי k. </p><p><b>הערה</b>: האלגוריתם אינו תחליף לשיטות האנליטיות הרגילות (למשל טורים אינסופיים), שכן אינו מספק שיטה לחשב את הערכים הלוגריתמיים היסודיים, כך שלא ניתן "לדלג" על פיתוח טכניקות "עמוקות" יותר. </p> <div class="mw-heading mw-heading3"><h3 id="הממוצע_האריתמטי-גאומטרי"><span id=".D7.94.D7.9E.D7.9E.D7.95.D7.A6.D7.A2_.D7.94.D7.90.D7.A8.D7.99.D7.AA.D7.9E.D7.98.D7.99-.D7.92.D7.90.D7.95.D7.9E.D7.98.D7.A8.D7.99"></span>הממוצע האריתמטי-גאומטרי</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D7%9C%D7%95%D7%92%D7%A8%D7%99%D7%AA%D7%9D&action=edit&section=6" title="עריכת קוד המקור של הפרק: הממוצע האריתמטי-גאומטרי"><span>עריכת קוד מקור</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D7%9C%D7%95%D7%92%D7%A8%D7%99%D7%AA%D7%9D&veaction=edit&section=6" title="עריכת פסקה: "הממוצע האריתמטי-גאומטרי"" class="mw-editsection-visualeditor"><span>עריכה</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/%D7%94%D7%9E%D7%9E%D7%95%D7%A6%D7%A2_%D7%94%D7%90%D7%A8%D7%99%D7%AA%D7%9E%D7%98%D7%99-%D7%92%D7%90%D7%95%D7%9E%D7%98%D7%A8%D7%99" class="mw-redirect" title="הממוצע האריתמטי-גאומטרי">הממוצע האריתמטי-גאומטרי</a> מספק קירובים מהירים ועתירי דיוק ללוגריתם הטבעי. החוקרים Sasaki ו-Kanada הראו ב-1982 שקירובים המבוססים על הממוצע האריתמטי גאומטרי מהירים במיוחד עבור דיוק בין 400 ל-1000 ספרות עשרוניות, בעוד ששיטות המבוססות על <a href="/wiki/%D7%98%D7%95%D7%A8_%D7%98%D7%99%D7%99%D7%9C%D7%95%D7%A8" title="טור טיילור">טור טיילור</a> הן מהירות יותר כאשר נדרש פחות דיוק. בעבודתם (ln(x מקורב לדיוק של <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 2^{-p}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi>p</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2^{-p}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/91b1f8a102947b3b5cf547521ac8f435ed829c78" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.5ex; height:2.509ex;" alt="{\displaystyle 2^{-p}}"></span> בעזרת הנוסחה הבאה (הודות ל<a href="/wiki/%D7%A7%D7%A8%D7%9C_%D7%A4%D7%A8%D7%99%D7%93%D7%A8%D7%99%D7%9A_%D7%92%D7%90%D7%95%D7%A1" title="קרל פרידריך גאוס">קרל פרידריך גאוס</a>): </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ln(x)\approx {\frac {\pi }{2M(1,2^{2-m}/x)}}-m\ln(2)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ln</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>≈</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>π</mi> <mrow> <mn>2</mn> <mi>M</mi> <mo stretchy="false">(</mo> <mn>1</mn> <mo>,</mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mo>−</mo> <mi>m</mi> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mo>−</mo> <mi>m</mi> <mi>ln</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ln(x)\approx {\frac {\pi }{2M(1,2^{2-m}/x)}}-m\ln(2)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/957e18641752c9fa7bf187811cd4a33e39aa0407" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:34.232ex; height:5.676ex;" alt="{\displaystyle \ln(x)\approx {\frac {\pi }{2M(1,2^{2-m}/x)}}-m\ln(2)}"></span> </p><p>כאשר m נבחר כך ש-<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x\,2^{m}>2^{p/2}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mspace width="thinmathspace" /> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msup> <mo>></mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mrow> </msup> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x\,2^{m}>2^{p/2}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a8515c12450df510f4199e003f7dc443f9fac2a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:11.905ex; height:2.843ex;" alt="{\displaystyle x\,2^{m}>2^{p/2}\,}"></span> כדי להבטיח את הדיוק הדרוש. </p> <div class="mw-heading mw-heading2"><h2 id="ראו_גם"><span id=".D7.A8.D7.90.D7.95_.D7.92.D7.9D"></span>ראו גם</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D7%9C%D7%95%D7%92%D7%A8%D7%99%D7%AA%D7%9D&action=edit&section=7" title="עריכת קוד המקור של הפרק: ראו גם"><span>עריכת קוד מקור</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D7%9C%D7%95%D7%92%D7%A8%D7%99%D7%AA%D7%9D&veaction=edit&section=7" title="עריכת פסקה: "ראו גם"" class="mw-editsection-visualeditor"><span>עריכה</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/%D7%A1%D7%A7%D7%90%D7%9C%D7%94_%D7%9C%D7%95%D7%92%D7%A8%D7%99%D7%AA%D7%9E%D7%99%D7%AA" title="סקאלה לוגריתמית">סקאלה לוגריתמית</a></li> <li><a href="/wiki/%D7%9C%D7%95%D7%92%D7%A8%D7%99%D7%AA%D7%9D_%D7%97%D7%95%D7%96%D7%A8" title="לוגריתם חוזר">לוגריתם חוזר</a></li> <li><a href="/wiki/%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%94_%D7%9E%D7%A2%D7%A8%D7%99%D7%9B%D7%99%D7%AA" title="פונקציה מעריכית">פונקציה מעריכית</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="קישורים_חיצוניים"><span id=".D7.A7.D7.99.D7.A9.D7.95.D7.A8.D7.99.D7.9D_.D7.97.D7.99.D7.A6.D7.95.D7.A0.D7.99.D7.99.D7.9D"></span>קישורים חיצוניים</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D7%9C%D7%95%D7%92%D7%A8%D7%99%D7%AA%D7%9D&action=edit&section=8" title="עריכת קוד המקור של הפרק: קישורים חיצוניים"><span>עריכת קוד מקור</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D7%9C%D7%95%D7%92%D7%A8%D7%99%D7%AA%D7%9D&veaction=edit&section=8" title="עריכת פסקה: "קישורים חיצוניים"" class="mw-editsection-visualeditor"><span>עריכה</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="sistersitebox plainlinks noprint" style="margin: 0 1em 0.5em 0;float: left;"><tbody><tr><th style="text-align:center">מיזמי <a href="/wiki/%D7%A7%D7%A8%D7%9F_%D7%95%D7%99%D7%A7%D7%99%D7%9E%D7%93%D7%99%D7%94" title="קרן ויקימדיה">קרן ויקימדיה</a></th></tr><tr><td><div class="sisterwikilinkT"><span typeof="mw:File"><span title="ויקימילון"><img alt="ויקימילון" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/24/Wiktionary-logo-he.png/20px-Wiktionary-logo-he.png" decoding="async" width="20" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/24/Wiktionary-logo-he.png/30px-Wiktionary-logo-he.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/24/Wiktionary-logo-he.png/40px-Wiktionary-logo-he.png 2x" data-file-width="135" data-file-height="135" /></span></span> ערך מילוני בוויקימילון: <b><a href="https://he.wiktionary.org/wiki/%D7%9C%D7%95%D7%92%D7%A8%D7%99%D7%AA%D7%9D" class="extiw" title="wikt:לוגריתם">לוגריתם</a></b></div></td></tr><tr><td><div class="sisterwikilinkT"><span typeof="mw:File"><span title="ויקיספר"><img alt="ויקיספר" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikibooks-logo.svg/20px-Wikibooks-logo.svg.png" decoding="async" width="20" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikibooks-logo.svg/30px-Wikibooks-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikibooks-logo.svg/40px-Wikibooks-logo.svg.png 2x" data-file-width="300" data-file-height="300" /></span></span> ספר לימוד בוויקיספר: <b><a href="https://he.wikibooks.org/wiki/%D7%9E%D7%AA%D7%9E%D7%98%D7%99%D7%A7%D7%94_%D7%AA%D7%99%D7%9B%D7%95%D7%A0%D7%99%D7%AA/%D7%90%D7%9C%D7%92%D7%91%D7%A8%D7%94_%D7%AA%D7%99%D7%9B%D7%95%D7%A0%D7%99%D7%AA/%D7%9E%D7%A2%D7%A8%D7%99%D7%9B%D7%99%D7%9D_%D7%95%D7%9C%D7%95%D7%92%D7%A8%D7%99%D7%AA%D7%9E%D7%99%D7%9D" class="extiw" title="b:מתמטיקה תיכונית/אלגברה תיכונית/מעריכים ולוגריתמים">לוגריתמים (אלגברה)</a></b></div></td></tr><tr><td><div class="sisterwikilinkT"><span typeof="mw:File"><span title="ויקישיתוף"><img alt="ויקישיתוף" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/20px-Commons-logo.svg.png" decoding="async" width="20" height="27" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/40px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span> תמונות ומדיה בוויקישיתוף: <b><a href="https://commons.wikimedia.org/wiki/Category:Logarithm" class="extiw" title="commons:Category:Logarithm">לוגריתם</a></b></div></td></tr></tbody></table><style data-mw-deduplicate="TemplateStyles:r36773993">.mw-parser-output .sistersitebox{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:#f9f9f9}</style> <ul><li>צחי אבנור, <span typeof="mw:File"><span title="קובץ PDF"><img alt="קובץ PDF" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/PDF_icon.svg/14px-PDF_icon.svg.png" decoding="async" width="14" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/PDF_icon.svg/21px-PDF_icon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6c/PDF_icon.svg/28px-PDF_icon.svg.png 2x" data-file-width="512" data-file-height="585" /></span></span> <a href="/wiki/%D7%A7%D7%95%D7%91%D7%A5:Logarithm-cc-by-Zachi-Evenor.pdf" title="קובץ:Logarithm-cc-by-Zachi-Evenor.pdf">לוגריתם</a> - הגדרות, תכונות והוכחות (קובץ <a href="/wiki/PDF" title="PDF">PDF</a> על שרת ויקיפדיה)</li> <li>גדי אלכסנדרוביץ', <a rel="nofollow" class="external text" href="https://gadial.net/2020/06/08/what_are_logarithms">מה זה לוגריתמים ובשביל מה זה טוב?</a>, באתר "לא מדויק", 8 ביוני 2020</li> <li><a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=N-7tcTIrers">How I Feel About Logarithms</a> – סרטון הסבר של <a rel="nofollow" class="external text" href="https://www.youtube.com/channel/UCOGeU-1Fig3rrDjhm9Zs_wg">Vi Hart</a> על לוגריתמים <span dir="rtl" class="languageicon">(באנגלית)</span><style data-mw-deduplicate="TemplateStyles:r36549940">.mw-parser-output .languageicon{font-size:0.95em;font-weight:bold;color:#555}</style> <span typeof="mw:File"><span title="סרטונים"><img alt="סרטונים" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1d/Gnome-video-x-generic.svg/15px-Gnome-video-x-generic.svg.png" decoding="async" width="15" height="15" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1d/Gnome-video-x-generic.svg/23px-Gnome-video-x-generic.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1d/Gnome-video-x-generic.svg/30px-Gnome-video-x-generic.svg.png 2x" data-file-width="48" data-file-height="48" /></span></span></li> <li><a rel="nofollow" class="external text" href="https://mathworld.wolfram.com/Logarithm.html">לוגריתם</a>, באתר <a href="/wiki/MathWorld" title="MathWorld">MathWorld</a> <span dir="rtl" class="languageicon">(באנגלית)</span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r36549940"></li> <li><a rel="nofollow" class="external text" href="https://www.britannica.com/science/logarithm">לוגריתם</a>, באתר <a href="/wiki/%D7%90%D7%A0%D7%A6%D7%99%D7%A7%D7%9C%D7%95%D7%A4%D7%93%D7%99%D7%94_%D7%91%D7%A8%D7%99%D7%98%D7%A0%D7%99%D7%A7%D7%94" title="אנציקלופדיה בריטניקה">אנציקלופדיה בריטניקה</a> <span dir="rtl" class="languageicon">(באנגלית)</span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r36549940"></li> <li><span typeof="mw:File"><a href="/wiki/%D7%A7%D7%95%D7%91%D7%A5:National_Library_IL_logo.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/df/National_Library_IL_logo.svg/20px-National_Library_IL_logo.svg.png" decoding="async" width="20" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/df/National_Library_IL_logo.svg/30px-National_Library_IL_logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/df/National_Library_IL_logo.svg/40px-National_Library_IL_logo.svg.png 2x" data-file-width="512" data-file-height="397" /></a></span> <a rel="nofollow" class="external text" href="https://www.nli.org.il/he/a-topic/987007533701405171">לוגריתמים</a>, דף שער ב<a href="/wiki/%D7%94%D7%A1%D7%A4%D7%A8%D7%99%D7%99%D7%94_%D7%94%D7%9C%D7%90%D7%95%D7%9E%D7%99%D7%AA" title="הספרייה הלאומית">ספרייה הלאומית</a></li></ul> <div role="navigation" class="navbox authority-control" aria-labelledby="בקרת_זהויות_15px&#124;link=https&#58;//www.wikidata.org/wiki/Q11197?uselang=he&#124;עריכת_הנתון_בוויקינתונים" style="padding:3px"><table class="nowraplinks hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th id="בקרת_זהויות_15px&#124;link=https&#58;//www.wikidata.org/wiki/Q11197?uselang=he&#124;עריכת_הנתון_בוויקינתונים" scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%D7%A2%D7%96%D7%A8%D7%94:%D7%91%D7%A7%D7%A8%D7%AA_%D7%96%D7%94%D7%95%D7%99%D7%95%D7%AA" title="עזרה:בקרת זהויות">בקרת זהויות</a> <span typeof="mw:File"><a href="https://www.wikidata.org/wiki/Q11197?uselang=he" title="עריכת הנתון בוויקינתונים"><img alt="עריכת הנתון בוויקינתונים" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Blue_pencil_RTL.svg/15px-Blue_pencil_RTL.svg.png" decoding="async" width="15" height="15" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Blue_pencil_RTL.svg/23px-Blue_pencil_RTL.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Blue_pencil_RTL.svg/30px-Blue_pencil_RTL.svg.png 2x" data-file-width="600" data-file-height="600" /></a></span></th><td class="navbox-list navbox-odd" style="text-align:left;border-right-width:2px;border-right-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"><div dir="ltr"> <ul><li><span class="nowrap"><a href="/wiki/%D7%94%D7%A1%D7%A4%D7%A8%D7%99%D7%99%D7%94_%D7%94%D7%9C%D7%90%D7%95%D7%9E%D7%99%D7%AA" title="הספרייה הלאומית">NLI</a>: <span class="uid"><a rel="nofollow" class="external text" href="http://olduli.nli.org.il/F/?func=find-b&local_base=NLX10&find_code=UID&request=987007533701405171">987007533701405171</a></span></span></li> <li><span class="nowrap"><a href="/wiki/%D7%94%D7%A1%D7%A4%D7%A8%D7%99%D7%99%D7%94_%D7%94%D7%9C%D7%90%D7%95%D7%9E%D7%99%D7%AA_%D7%A9%D7%9C_%D7%A1%D7%A4%D7%A8%D7%93" title="הספרייה הלאומית של ספרד">BNE</a>: <span class="uid"><a rel="nofollow" class="external text" href="http://catalogo.bne.es/uhtbin/authoritybrowse.cgi?action=display&authority_id=XX527539">XX527539</a></span></span></li> <li><span class="nowrap"><a href="/wiki/%D7%94%D7%A1%D7%A4%D7%A8%D7%99%D7%99%D7%94_%D7%94%D7%9C%D7%90%D7%95%D7%9E%D7%99%D7%AA_%D7%A9%D7%9C_%D7%A6%D7%A8%D7%A4%D7%AA" title="הספרייה הלאומית של צרפת">BnF</a>: <span class="uid"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb11941516p">cb11941516p</a> <a rel="nofollow" class="external text" href="https://data.bnf.fr/ark:/12148/cb11941516p">(data)</a></span></span></li> <li><span class="nowrap"><a href="/wiki/%D7%A7%D7%95%D7%91%D7%A5_%D7%91%D7%A7%D7%A8%D7%94_%D7%9E%D7%A9%D7%95%D7%9C%D7%91" title="קובץ בקרה משולב">GND</a>: <span class="uid"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/4168047-9">4168047-9</a></span></span></li> <li><span class="nowrap"><a href="/wiki/%D7%A9%D7%99%D7%98%D7%AA_%D7%A1%D7%A4%D7%A8%D7%99%D7%99%D7%AA_%D7%94%D7%A7%D7%95%D7%A0%D7%92%D7%A8%D7%A1" title="שיטת ספריית הקונגרס">LCCN</a>: <span class="uid"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/subjects/sh85078091">sh85078091</a></span></span></li> <li><span class="nowrap"><a href="/wiki/%D7%A1%D7%A4%D7%A8%D7%99%D7%99%D7%AA_%D7%94%D7%93%D7%99%D7%90%D7%98_%D7%94%D7%9C%D7%90%D7%95%D7%9E%D7%99%D7%AA" title="ספריית הדיאט הלאומית">NDL</a>: <span class="uid"><a rel="nofollow" class="external text" href="https://id.ndl.go.jp/auth/ndlna/00572566">00572566</a></span></span></li></ul> </div></div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">אוחזר מתוך "<a dir="ltr" href="https://he.wikipedia.org/w/index.php?title=לוגריתם&oldid=38539851">https://he.wikipedia.org/w/index.php?title=לוגריתם&oldid=38539851</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/%D7%95%D7%99%D7%A7%D7%99%D7%A4%D7%93%D7%99%D7%94:%D7%A7%D7%98%D7%92%D7%95%D7%A8%D7%99%D7%94" title="ויקיפדיה:קטגוריה">קטגוריות</a>: <ul><li><a href="/wiki/%D7%A7%D7%98%D7%92%D7%95%D7%A8%D7%99%D7%94:%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%95%D7%AA_%D7%9E%D7%9E%D7%A9%D7%99%D7%95%D7%AA_%D7%95%D7%9E%D7%A8%D7%95%D7%9B%D7%91%D7%95%D7%AA" title="קטגוריה:פונקציות ממשיות ומרוכבות">פונקציות ממשיות ומרוכבות</a></li><li><a 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