Alugaritm agaman — Wikipedia

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vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Aydatn"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Aydatn</span> </div> </a> <button aria-controls="toc-Aydatn-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>Afficher / masquer la sous-section Aydatn</span> </button> <ul id="toc-Aydatn-sublist" class="vector-toc-list"> <li id="toc-Taɣlalt_d_tsbk_n_tasɣnt_n_ulugaritm_agaman" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Taɣlalt_d_tsbk_n_tasɣnt_n_ulugaritm_agaman"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Taɣlalt d tsbk n tasɣnt n ulugaritm agaman</span> </div> </a> <ul id="toc-Taɣlalt_d_tsbk_n_tasɣnt_n_ulugaritm_agaman-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Timhal_f_tasɣnt_n_ulugaritm_agaman" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Timhal_f_tasɣnt_n_ulugaritm_agaman"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Timhal f tasɣnt n ulugaritm agaman</span> </div> </a> <ul id="toc-Timhal_f_tasɣnt_n_ulugaritm_agaman-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Aydatn_yaḍnin" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Aydatn_yaḍnin"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Aydatn yaḍnin</span> </div> </a> <ul id="toc-Aydatn_yaḍnin-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Amawal" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Amawal"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Amawal</span> </div> </a> <ul id="toc-Amawal-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Isaɣuln" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Isaɣuln"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Isaɣuln</span> </div> </a> <ul id="toc-Isaɣuln-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="Sommaire" 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="Basculer la table des matières" > <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">Basculer la table des matières</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">Alugaritm agaman</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="Aller à un article dans une autre langue. Disponible en 61 langues." > <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-61" 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">61 tutlayin</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Natuurlike_logaritme" title="Natuurlike logaritme – afrikaans" lang="af" hreflang="af" data-title="Natuurlike logaritme" data-language-autonym="Afrikaans" data-language-local-name="afrikaans" class="interlanguage-link-target"><span>Afrikaans</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_%D8%B7%D8%A8%D9%8A%D8%B9%D9%8A" title="لوغاريتم طبيعي – ⵜⴰⵄⵔⴰⴱⵜ" lang="ar" hreflang="ar" data-title="لوغاريتم طبيعي" data-language-autonym="العربية" data-language-local-name="ⵜⴰⵄⵔⴰⴱⵜ" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Natural_loqarifm" title="Natural loqarifm – azerbaïdjanais" lang="az" hreflang="az" data-title="Natural loqarifm" data-language-autonym="Azərbaycanca" data-language-local-name="azerbaïdjanais" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9D%D0%B0%D1%82%D1%83%D1%80%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B_%D0%BB%D0%B0%D0%B3%D0%B0%D1%80%D1%8B%D1%84%D0%BC" title="Натуральны лагарыфм – ⵜⴰⴱⵉⵍⴰⵔⵓⵙⵜ" lang="be" hreflang="be" data-title="Натуральны лагарыфм" data-language-autonym="Беларуская" data-language-local-name="ⵜⴰⴱⵉⵍⴰⵔⵓⵙⵜ" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9D%D0%B0%D1%82%D1%83%D1%80%D0%B0%D0%BB%D0%B5%D0%BD_%D0%BB%D0%BE%D0%B3%D0%B0%D1%80%D0%B8%D1%82%D1%8A%D0%BC" title="Натурален логаритъм – ⵜⴰⴱⵍⵖⴰⵔⵉⵜ" lang="bg" hreflang="bg" data-title="Натурален логаритъм" data-language-autonym="Български" data-language-local-name="ⵜⴰⴱⵍⵖⴰⵔⵉⵜ" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-br mw-list-item"><a href="https://br.wikipedia.org/wiki/Logaritm_neperian" title="Logaritm neperian – breton" lang="br" hreflang="br" data-title="Logaritm neperian" data-language-autonym="Brezhoneg" data-language-local-name="breton" 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/Prirodni_logaritam" title="Prirodni logaritam – bosniaque" lang="bs" hreflang="bs" data-title="Prirodni logaritam" data-language-autonym="Bosanski" data-language-local-name="bosniaque" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Logaritme_natural" title="Logaritme natural – catalan" lang="ca" hreflang="ca" data-title="Logaritme natural" data-language-autonym="Català" data-language-local-name="catalan" 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%DB%8C_%D8%B3%D8%B1%D9%88%D8%B4%D8%AA%DB%8C" title="لۆگاریتمی سروشتی – sorani" lang="ckb" hreflang="ckb" data-title="لۆگاریتمی سروشتی" data-language-autonym="کوردی" data-language-local-name="sorani" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%9D%D0%B0%D1%82%D1%83%D1%80%D0%B0%D0%BB%D0%BB%C4%83_%D0%BB%D0%BE%D0%B3%D0%B0%D1%80%D0%B8%D1%84%D0%BC" title="Натураллă логарифм – tchouvache" lang="cv" hreflang="cv" data-title="Натураллă логарифм" data-language-autonym="Чӑвашла" data-language-local-name="tchouvache" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Naturlig_logaritme" title="Naturlig logaritme – danois" lang="da" hreflang="da" data-title="Naturlig logaritme" data-language-autonym="Dansk" data-language-local-name="danois" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de badge-Q70894304 mw-list-item" title=""><a href="https://de.wikipedia.org/wiki/Nat%C3%BCrlicher_Logarithmus" title="Natürlicher Logarithmus – ⵜⴰⵍⵉⵎⴰⵏⵜ" lang="de" hreflang="de" data-title="Natürlicher Logarithmus" data-language-autonym="Deutsch" data-language-local-name="ⵜⴰⵍⵉⵎⴰⵏⵜ" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A6%CF%85%CF%83%CE%B9%CE%BA%CF%8C%CF%82_%CE%BB%CE%BF%CE%B3%CE%AC%CF%81%CE%B9%CE%B8%CE%BC%CE%BF%CF%82" title="Φυσικός λογάριθμος – ⵜⴰⴳⵔⵉⴳⵉⵜ" lang="el" hreflang="el" data-title="Φυσικός λογάριθμος" data-language-autonym="Ελληνικά" data-language-local-name="ⵜⴰⴳⵔⵉⴳⵉⵜ" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Natural_logarithm" title="Natural logarithm – ⵜⴰⵏⴳⵍⵉⵣⵜ" lang="en" hreflang="en" data-title="Natural logarithm" data-language-autonym="English" data-language-local-name="ⵜⴰⵏⴳⵍⵉⵣⵜ" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Logaritmo_natural" title="Logaritmo natural – ⵜⴰⵙⴱⵏⵢⵓⵍⵉⵜ" lang="es" hreflang="es" data-title="Logaritmo natural" data-language-autonym="Español" data-language-local-name="ⵜⴰⵙⴱⵏⵢⵓⵍⵉⵜ" 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/Naturaallogaritm" title="Naturaallogaritm – estonien" lang="et" hreflang="et" data-title="Naturaallogaritm" data-language-autonym="Eesti" data-language-local-name="estonien" 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_natural" title="Logaritmo natural – basque" lang="eu" hreflang="eu" data-title="Logaritmo natural" data-language-autonym="Euskara" data-language-local-name="basque" class="interlanguage-link-target"><span>Euskara</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_%D8%B7%D8%A8%DB%8C%D8%B9%DB%8C" title="لگاریتم طبیعی – ⵜⴰⴼⵓⵔⵙⵉⵜ" lang="fa" hreflang="fa" data-title="لگاریتم طبیعی" data-language-autonym="فارسی" data-language-local-name="ⵜⴰⴼⵓⵔⵙⵉⵜ" 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/Luonnollinen_logaritmi" title="Luonnollinen logaritmi – finnois" lang="fi" hreflang="fi" data-title="Luonnollinen logaritmi" data-language-autonym="Suomi" data-language-local-name="finnois" 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/N%C3%A1tt%C3%BArlig_logaritma" title="Náttúrlig logaritma – féroïen" lang="fo" hreflang="fo" data-title="Náttúrlig logaritma" data-language-autonym="Føroyskt" data-language-local-name="féroïen" 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_n%C3%A9p%C3%A9rien" title="Logarithme népérien – ⵜⴰⴼⵔⴰⵏⵙⵉⵙⵜ" lang="fr" hreflang="fr" data-title="Logarithme népérien" data-language-autonym="Français" data-language-local-name="ⵜⴰⴼⵔⴰⵏⵙⵉⵙⵜ" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Logaritmo_natural" title="Logaritmo natural – galicien" lang="gl" hreflang="gl" data-title="Logaritmo natural" data-language-autonym="Galego" data-language-local-name="galicien" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/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 – hébreu" lang="he" hreflang="he" data-title="לוגריתם טבעי" data-language-autonym="עברית" data-language-local-name="hébreu" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%BE%E0%A4%95%E0%A5%83%E0%A4%A4%E0%A4%BF%E0%A4%95_%E0%A4%B2%E0%A4%98%E0%A5%81%E0%A4%97%E0%A4%A3%E0%A4%95" title="प्राकृतिक लघुगणक – ⵜⴰⵀⵉⵏⴷⵉⵜ" lang="hi" hreflang="hi" data-title="प्राकृतिक लघुगणक" data-language-autonym="हिन्दी" data-language-local-name="ⵜⴰⵀⵉⵏⴷⵉⵜ" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Term%C3%A9szetes_logaritmus" title="Természetes logaritmus – ⵜⴰⵀⵏⵖⴰⵔⵉⵜ" lang="hu" hreflang="hu" data-title="Természetes logaritmus" data-language-autonym="Magyar" data-language-local-name="ⵜⴰⵀⵏⵖⴰⵔⵉⵜ" 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%B2%D5%B6%D5%A1%D5%AF%D5%A1%D5%B6_%D5%AC%D5%B8%D5%A3%D5%A1%D6%80%D5%AB%D5%A9%D5%B4" title="Բնական լոգարիթմ – arménien" lang="hy" hreflang="hy" data-title="Բնական լոգարիթմ" data-language-autonym="Հայերեն" data-language-local-name="arménien" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Logaritma_alami" title="Logaritma alami – ⵜⴰⵏⴷⵓⵏⵉⵙⵉⵜ" lang="id" hreflang="id" data-title="Logaritma alami" data-language-autonym="Bahasa Indonesia" data-language-local-name="ⵜⴰⵏⴷⵓⵏⵉⵙⵉⵜ" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Logaritmo_naturale" title="Logaritmo naturale – ⵜⴰⵟⴰⵍⵢⴰⵏⵜ" lang="it" hreflang="it" data-title="Logaritmo naturale" data-language-autonym="Italiano" data-language-local-name="ⵜⴰⵟⴰⵍⵢⴰⵏⵜ" 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/%E8%87%AA%E7%84%B6%E5%AF%BE%E6%95%B0" title="自然対数 – ⵜⴰⵊⴰⴱⴱⵓⵏⵉⵜ" lang="ja" hreflang="ja" data-title="自然対数" data-language-autonym="日本語" data-language-local-name="ⵜⴰⵊⴰⴱⴱⵓⵏⵉⵜ" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%9C%E1%83%90%E1%83%A2%E1%83%A3%E1%83%A0%E1%83%90%E1%83%9A%E1%83%A3%E1%83%A0%E1%83%98_%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="ნატურალური ლოგარითმი – géorgien" lang="ka" hreflang="ka" data-title="ნატურალური ლოგარითმი" data-language-autonym="ქართული" data-language-local-name="géorgien" 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%9D%D0%B0%D1%82%D1%83%D1%80%D0%B0%D0%BB_%D0%BB%D0%BE%D0%B3%D0%B0%D1%80%D0%B8%D1%84%D0%BC" title="Натурал логарифм – kazakh" lang="kk" hreflang="kk" data-title="Натурал логарифм" data-language-autonym="Қазақша" data-language-local-name="kazakh" 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/%EC%9E%90%EC%97%B0%EB%A1%9C%EA%B7%B8" title="자연로그 – ⵜⴰⴽⵓⵔⵉⵜ" lang="ko" hreflang="ko" data-title="자연로그" data-language-autonym="한국어" data-language-local-name="ⵜⴰⴽⵓⵔⵉⵜ" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Logaritm_natural" title="Logaritm natural – lombard" lang="lmo" hreflang="lmo" data-title="Logaritm natural" data-language-autonym="Lombard" data-language-local-name="lombard" 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/Nat%C5%ABrinis_logaritmas" title="Natūrinis logaritmas – lituanien" lang="lt" hreflang="lt" data-title="Natūrinis logaritmas" data-language-autonym="Lietuvių" data-language-local-name="lituanien" 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/Natur%C4%81lais_logaritms" title="Naturālais logaritms – letton" lang="lv" hreflang="lv" data-title="Naturālais logaritms" data-language-autonym="Latviešu" data-language-local-name="letton" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9F%D1%80%D0%B8%D1%80%D0%BE%D0%B4%D0%B5%D0%BD_%D0%BB%D0%BE%D0%B3%D0%B0%D1%80%D0%B8%D1%82%D0%B0%D0%BC" title="Природен логаритам – macédonien" lang="mk" hreflang="mk" data-title="Природен логаритам" data-language-autonym="Македонски" data-language-local-name="macédonien" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Logaritma_asli" title="Logaritma asli – ⵜⴰⵎⴰⵍⴰⵡⵉⵜ" lang="ms" hreflang="ms" data-title="Logaritma asli" data-language-autonym="Bahasa Melayu" data-language-local-name="ⵜⴰⵎⴰⵍⴰⵡⵉⵜ" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Natuurlijke_logaritme" title="Natuurlijke logaritme – ⵜⴰⵀⵓⵍⴰⵏⴷⵉⵜ" lang="nl" hreflang="nl" data-title="Natuurlijke logaritme" data-language-autonym="Nederlands" data-language-local-name="ⵜⴰⵀⵓⵍⴰⵏⴷⵉⵜ" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Naturlig_logaritme" title="Naturlig logaritme – norvégien bokmål" lang="nb" hreflang="nb" data-title="Naturlig logaritme" data-language-autonym="Norsk bokmål" data-language-local-name="norvégien bokmål" 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_neperian" title="Logaritme neperian – occitan" lang="oc" hreflang="oc" data-title="Logaritme neperian" data-language-autonym="Occitan" data-language-local-name="occitan" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Logarytm_naturalny" title="Logarytm naturalny – ⵜⴰⴱⵓⵍⵓⵏⵉⵜ" lang="pl" hreflang="pl" data-title="Logarytm naturalny" data-language-autonym="Polski" data-language-local-name="ⵜⴰⴱⵓⵍⵓⵏⵉⵜ" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Logaritm_%C3%ABd_Napier" title="Logaritm ëd Napier – piémontais" lang="pms" hreflang="pms" data-title="Logaritm ëd Napier" data-language-autonym="Piemontèis" data-language-local-name="piémontais" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Logaritmo_natural" title="Logaritmo natural – ⵜⴰⴱⵕⵟⵇⵉⵣⵜ" lang="pt" hreflang="pt" data-title="Logaritmo natural" data-language-autonym="Português" data-language-local-name="ⵜⴰⴱⵕⵟⵇⵉⵣⵜ" 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_natural" title="Logaritm natural – ⵜⴰⵔⵓⵎⴰⵏⵉⵜ" lang="ro" hreflang="ro" data-title="Logaritm natural" data-language-autonym="Română" data-language-local-name="ⵜⴰⵔⵓⵎⴰⵏⵉⵜ" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9D%D0%B0%D1%82%D1%83%D1%80%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B%D0%B9_%D0%BB%D0%BE%D0%B3%D0%B0%D1%80%D0%B8%D1%84%D0%BC" title="Натуральный логарифм – ⵜⴰⵔⵓⵙⵉⵜ" lang="ru" hreflang="ru" data-title="Натуральный логарифм" data-language-autonym="Русский" data-language-local-name="ⵜⴰⵔⵓⵙⵉⵜ" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Prirodni_logaritam" title="Prirodni logaritam – serbo-croate" lang="sh" hreflang="sh" data-title="Prirodni logaritam" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbo-croate" 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%B4%E0%B7%8A%E2%80%8D%E0%B6%BB%E0%B6%9A%E0%B7%98%E0%B6%AD%E0%B7%92_%E0%B6%BD%E0%B6%9D%E0%B7%94%E0%B6%9C%E0%B6%AB%E0%B6%9A" title="ප්‍රකෘති ලඝුගණක – cingalais" lang="si" hreflang="si" data-title="ප්‍රකෘති ලඝුගණක" data-language-autonym="සිංහල" data-language-local-name="cingalais" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Naravni_logaritem" title="Naravni logaritem – slovène" lang="sl" hreflang="sl" data-title="Naravni logaritem" data-language-autonym="Slovenščina" data-language-local-name="slovène" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Logaritmi_natyror" title="Logaritmi natyror – albanais" lang="sq" hreflang="sq" data-title="Logaritmi natyror" data-language-autonym="Shqip" data-language-local-name="albanais" 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%9F%D1%80%D0%B8%D1%80%D0%BE%D0%B4%D0%BD%D0%B8_%D0%BB%D0%BE%D0%B3%D0%B0%D1%80%D0%B8%D1%82%D0%B0%D0%BC" title="Природни логаритам – serbe" lang="sr" hreflang="sr" data-title="Природни логаритам" data-language-autonym="Српски / srpski" data-language-local-name="serbe" 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/Naturliga_logaritmen" title="Naturliga logaritmen – ⵜⴰⵙⵡⵉⴷⵉⵜ" lang="sv" hreflang="sv" data-title="Naturliga logaritmen" data-language-autonym="Svenska" data-language-local-name="ⵜⴰⵙⵡⵉⴷⵉⵜ" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%87%E0%AE%AF%E0%AE%B2%E0%AF%8D_%E0%AE%AE%E0%AE%9F%E0%AE%95%E0%AF%8D%E0%AE%95%E0%AF%88" title="இயல் மடக்கை – ⵜⴰⵜⴰⵎⵉⵍⵜ" lang="ta" hreflang="ta" data-title="இயல் மடக்கை" data-language-autonym="தமிழ்" data-language-local-name="ⵜⴰⵜⴰⵎⵉⵍⵜ" 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%E0%B8%98%E0%B8%A3%E0%B8%A3%E0%B8%A1%E0%B8%8A%E0%B8%B2%E0%B8%95%E0%B8%B4" title="ลอการิทึมธรรมชาติ – ⵜⴰⵜⴰⵢⵍⴰⵏⴷⵉⵜ" lang="th" hreflang="th" data-title="ลอการิทึมธรรมชาติ" data-language-autonym="ไทย" data-language-local-name="ⵜⴰⵜⴰⵢⵍⴰⵏⴷⵉⵜ" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9D%D0%B0%D1%82%D1%83%D1%80%D0%B0%D0%BB%D1%8C%D0%BD%D0%B8%D0%B9_%D0%BB%D0%BE%D0%B3%D0%B0%D1%80%D0%B8%D1%84%D0%BC" title="Натуральний логарифм – ⵜⵓⴽⵔⴰⵏⵉⵜ" lang="uk" hreflang="uk" data-title="Натуральний логарифм" data-language-autonym="Українська" data-language-local-name="ⵜⵓⴽⵔⴰⵏⵉⵜ" 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%82%D8%AF%D8%B1%D8%AA%DB%8C_%D9%84%D8%A7%DA%AF%D8%B1%D8%AA%DA%BE%D9%85" title="قدرتی لاگرتھم – ⵜⵓⵔⴷⵓⵜ" lang="ur" hreflang="ur" data-title="قدرتی لاگرتھم" data-language-autonym="اردو" data-language-local-name="ⵜⵓⵔⴷⵓⵜ" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Logarit_t%E1%BB%B1_nhi%C3%AAn" title="Logarit tự nhiên – ⵜⴰⴼⵉⵜⵏⴰⵎⵉⵜ" lang="vi" hreflang="vi" data-title="Logarit tự nhiên" data-language-autonym="Tiếng Việt" data-language-local-name="ⵜⴰⴼⵉⵜⵏⴰⵎⵉⵜ" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E8%87%AA%E7%84%B6%E5%AF%B9%E6%95%B0" title="自然对数 – wu" lang="wuu" hreflang="wuu" data-title="自然对数" data-language-autonym="吴语" data-language-local-name="wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E8%87%AA%E7%84%B6%E5%B0%8D%E6%95%B8" title="自然對數 – ⵜⴰⵛⵉⵏⵡⵉⵜ" lang="zh" hreflang="zh" data-title="自然對數" data-language-autonym="中文" data-language-local-name="ⵜⴰⵛⵉⵏⵡⵉⵜ" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E8%87%AA%E7%84%B6%E5%B0%8D%E6%95%B8" title="自然對數 – chinois littéraire" lang="lzh" hreflang="lzh" data-title="自然對數" data-language-autonym="文言" data-language-local-name="chinois littéraire" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Ch%C5%AB-ji%C3%A2n_t%C3%B9i-s%C3%B2%CD%98" title="Chū-jiân tùi-sò͘ – minnan" lang="nan" hreflang="nan" data-title="Chū-jiân tùi-sò͘" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="minnan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E8%87%AA%E7%84%B6%E5%B0%8D%E6%95%B8" title="自然對數 – cantonais" lang="yue" hreflang="yue" data-title="自然對數" data-language-autonym="粵語" data-language-local-name="cantonais" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a 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class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="shi" dir="ltr"><div style="font-size:100%;margin-top:20px;margin-bottom:20px;" align="center"> <table style="width:80%; margin-bottom:0px;"> <tbody><tr> <td class="globegris" style="background-repeat:no-repeat; background-position:-40px -15px; width:100%; border:1px solid #ff8822; vertical-align:top; -moz-border-radius: 10px; -webkit-border-radius: 10px; border-radius:0px;"> <table style="width:100%; margin-bottom:0px; vertical-align:top; font-size:95%; background:#ffeedd;"> <tbody><tr> <td> </td> <td> </td> <td><div style="text-align: center;"> <span typeof="mw:File"><a href="/wiki/Afaylu:2017-fr.wp-orange-source.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a1/2017-fr.wp-orange-source.svg/40px-2017-fr.wp-orange-source.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a1/2017-fr.wp-orange-source.svg/60px-2017-fr.wp-orange-source.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a1/2017-fr.wp-orange-source.svg/80px-2017-fr.wp-orange-source.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span> </div></td> <td> </td> <td> </td> <td> </td> <td> </td> <td><span style="font-size:94%"> <b>Amnni ad icqqa ad t tfhmt !</b></span><br /><span style="font-size:90%">Amnni ad gis kra n iwalwn nna ur iẓḍaṛ yan ad tn ifhm iɣ ur issin ɣ umawal iẓlin n tutlayt taclḥiyt tatrart.<br /><b>Mad igan afssay ?</b> Fad ad tfhmt mad gis illan tzḍart <b>ad tawst i yixf nnk s umawal</b> lli illan ɣ izddar akkʷ n tasna. Iɣ t ur tufit, tzḍart <b>ad nn taggʷt ɣ <a href="/wiki/Wikipidya:Izdayn_ifulkin" class="mw-redirect" title="Wikipidya:Izdayn ifulkin">imawaln d isgzawaln</a></b>.</span> </td></tr></tbody></table> </td></tr></tbody></table></div><figure typeof="mw:File/Thumb"><a href="/wiki/Afaylu:Logarithme_neperien.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/50/Logarithme_neperien.svg/325px-Logarithme_neperien.svg.png" decoding="async" width="325" height="233" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/50/Logarithme_neperien.svg/488px-Logarithme_neperien.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/50/Logarithme_neperien.svg/650px-Logarithme_neperien.svg.png 2x" data-file-width="604" data-file-height="433" /></a><figcaption>Alugaritm anipiri </figcaption></figure><p>Iga <b>Alugaritm agaman</b> nɣ <b>Alugaritm anipiri</b> (s <a href="/wiki/Tanglizt" class="mw-redirect" title="Tanglizt">tanglizt</a> : Natural logarithm) yat tsɣnt bahra ittyusann ɣ <a href="/wiki/Tusnakt" title="Tusnakt">tusnakt</a>. Ar tsnfal tasɣnt ad afaris s tmrnit zun d <a href="/w/index.php?title=Tas%C9%A3nt_talugaritm&action=edit&redlink=1" class="new" title="Tasɣnt talugaritm (ur tlli tasna ad)">tisɣnin ilugaritmiyn</a> yaḍnin. Ar tt nttara s mk ad : <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"> <mi>ln</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mo stretchy="false">)</mo> </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/ba402812c9973ae68ba7d44de83b26f4b9692480" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.749ex; height:2.843ex;" alt="{\displaystyle \ln()}"></span>. </p><p>Ar nttini is iga alugaritm agaman s uzadur n <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 e}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>e</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cd253103f0876afc68ebead27a5aa9867d927467" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.083ex; height:1.676ex;" alt="{\displaystyle e}"></span> acku <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(e)=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>l</mi> <mi>n</mi> <mo stretchy="false">(</mo> <mi>e</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ln(e)=1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/307803c026addf230fe82554150bdc7ecf54933a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.242ex; height:2.843ex;" alt="{\displaystyle ln(e)=1}"></span>. Iga alugaritm agaman tamnzut n tsɣnt : <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\longmapsto 1/x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo stretchy="false">⟼</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x\longmapsto 1/x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/21f400318a02abd1e444e7a764da7323e4edd62b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.08ex; height:2.843ex;" alt="{\displaystyle x\longmapsto 1/x}"></span> ɣ uzilal <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 ]0;+\infty [}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">]</mo> <mn>0</mn> <mo>;</mo> <mo>+</mo> <mi mathvariant="normal">∞</mi> <mo stretchy="false">[</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ]0;+\infty [}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9a2b9afa8192cc3f8173fadddad0d1f5c499d881" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.622ex; height:2.843ex;" alt="{\displaystyle ]0;+\infty [}"></span> . </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Amzruy">Amzruy</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Alugaritm_agaman&veaction=edit&section=1" title="Snfl tigzmi: Amzruy" class="mw-editsection-visualeditor"><span>ssnfl</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Alugaritm_agaman&action=edit&section=1" title="Modifier le code source de la section : Amzruy"><span>Snfl asagm</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Alugaritm ad dars yan yism yaḍn ad t igan d "anipiri". Ism ad ikka d <a href="/wiki/John_Napir" class="mw-redirect" title="John Napir">John Napir</a>, yan umusnak askatlandi, amskar amzwaru n tflwit talugaritmiyt (tmzaray f talli nssn). </p><p>Tettyawskar tazmilt n ulugaritm zɣ dar <a href="/w/index.php?title=Gr%C3%A9goire_de_Saint-Vincent_d_Alphonse_Antonio_de_Sarasa&action=edit&redlink=1" class="new" title="Grégoire de Saint-Vincent d Alphonse Antonio de Sarasa (ur tlli tasna ad)">Grégoire de Saint-Vincent d Alphonse Antonio de Sarasa</a> ɣ usggʷas n 1649. </p> <div class="mw-heading mw-heading2"><h2 id="Isnmal">Isnmal</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Alugaritm_agaman&veaction=edit&section=2" title="Snfl tigzmi: Isnmal" class="mw-editsection-visualeditor"><span>ssnfl</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Alugaritm_agaman&action=edit&section=2" title="Modifier le code source de la section : Isnmal"><span>Snfl asagm</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Ad tili <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\in ]0;+\infty [}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>∈</mo> <mo stretchy="false">]</mo> <mn>0</mn> <mo>;</mo> <mo>+</mo> <mi mathvariant="normal">∞</mi> <mo stretchy="false">[</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a\in ]0;+\infty [}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b33d73dc2873c676cad660baddaeaaa446355d1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.047ex; height:2.843ex;" alt="{\displaystyle a\in ]0;+\infty [}"></span>, nzḍar ad nini mas d asnml n tsɣnt talugaritmiyt iga tt unrar lli illan ɣ izddar n tsɣnt n <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\mapsto 1/x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo stretchy="false">↦</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x\mapsto 1/x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/00cd4517889c7aae14fd456131a7e75c1ed61de9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.598ex; height:2.843ex;" alt="{\displaystyle x\mapsto 1/x}"></span> gr <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span> d 1. Ar tt nttara s tɣarast ad: </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Afaylu:Log-pole-x_1.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Log-pole-x_1.svg/220px-Log-pole-x_1.svg.png" decoding="async" width="220" height="110" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Log-pole-x_1.svg/330px-Log-pole-x_1.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Log-pole-x_1.svg/440px-Log-pole-x_1.svg.png 2x" data-file-width="601" data-file-height="301" /></a><figcaption>Tasɣnt talugaritm tga unrar lli illan ɣ izddar n tasɣnt <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\mapsto 1/x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo stretchy="false">↦</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x\mapsto 1/x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/00cd4517889c7aae14fd456131a7e75c1ed61de9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.598ex; height:2.843ex;" alt="{\displaystyle x\mapsto 1/x}"></span> gr <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span> d 1.</figcaption></figure> <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 a=\int _{1}^{a}{\frac {1}{x}}\,dx.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ln</mi> <mo>⁡</mo> <mi>a</mi> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>x</mi> </mfrac> </mrow> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ln a=\int _{1}^{a}{\frac {1}{x}}\,dx.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0643577384575f32c790c261f6bd4125c6a711c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:16.353ex; height:5.843ex;" alt="{\displaystyle \ln a=\int _{1}^{a}{\frac {1}{x}}\,dx.}"></span> </p><p>Iɣ darnɣ <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<1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo><</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a<1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7b8d3f65a187e46328021b646ee8769425a04d72" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.491ex; height:2.176ex;" alt="{\displaystyle a<1}"></span> rad nini mas d anrar lli darnɣ illan iga uzdir. </p><p>Tṭṭaf tasɣnt talugaritmiyt aydatn kullu tn n <a href="/w/index.php?title=Tas%C9%A3nt_talugaritmt&action=edit&redlink=1" class="new" title="Tasɣnt talugaritmt (ur tlli tasna ad)">tsɣnin tilugaritmin</a>.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </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="{\textstyle \ln(ab)=\ln a+\ln b.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>ln</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mi>b</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>ln</mi> <mo>⁡</mo> <mi>a</mi> <mo>+</mo> <mi>ln</mi> <mo>⁡</mo> <mi>b</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle \ln(ab)=\ln a+\ln b.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6d76680f24a9d1e202f23835dac552da6bdfe64d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:19.442ex; height:2.843ex;" alt="{\textstyle \ln(ab)=\ln a+\ln b.}"></span> </p><p>Nzḍar ad nml ayad s tibḍit n uɣrd lli f nsawl ɣ umzwaru s snat tfulin ɣ akud ann nɣrd s usnfl n umutti <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=ta}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>=</mo> <mi>t</mi> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x=ta}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/898bef5176cf2a1892523fc525e2c2a155e31b7b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.498ex; height:2.009ex;" alt="{\displaystyle x=ta}"></span> ɣ tfult tiss snat, zun d mk ad: </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 {\begin{aligned}\ln(ab)=\int _{1}^{ab}{\frac {1}{x}}\,dx&=\int _{1}^{a}{\frac {1}{x}}\,dx+\int _{a}^{ab}{\frac {1}{x}}\,dx\\[5pt]&=\int _{1}^{a}{\frac {1}{x}}\,dx+\int _{1}^{b}{\frac {1}{at}}\,d(at)\\[5pt]&=\int _{1}^{a}{\frac {1}{x}}\,dx+\int _{1}^{b}{\frac {1}{t}}\,dt\\[5pt]&=\ln a+\ln b.\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="0.8em 0.8em 0.8em 0.3em" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>ln</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mi>b</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> <mi>b</mi> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>x</mi> </mfrac> </mrow> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>x</mi> </mfrac> </mrow> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>+</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> <mi>b</mi> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>x</mi> </mfrac> </mrow> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>x</mi> </mfrac> </mrow> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>+</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>a</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mspace width="thinmathspace" /> <mi>d</mi> <mo stretchy="false">(</mo> <mi>a</mi> <mi>t</mi> <mo stretchy="false">)</mo> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>x</mi> </mfrac> </mrow> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>+</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>t</mi> </mfrac> </mrow> <mspace width="thinmathspace" /> <mi>d</mi> <mi>t</mi> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mi>ln</mi> <mo>⁡</mo> <mi>a</mi> <mo>+</mo> <mi>ln</mi> <mo>⁡</mo> <mi>b</mi> <mo>.</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}\ln(ab)=\int _{1}^{ab}{\frac {1}{x}}\,dx&=\int _{1}^{a}{\frac {1}{x}}\,dx+\int _{a}^{ab}{\frac {1}{x}}\,dx\\[5pt]&=\int _{1}^{a}{\frac {1}{x}}\,dx+\int _{1}^{b}{\frac {1}{at}}\,d(at)\\[5pt]&=\int _{1}^{a}{\frac {1}{x}}\,dx+\int _{1}^{b}{\frac {1}{t}}\,dt\\[5pt]&=\ln a+\ln b.\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8f2b53dd1976a99950b5c8217d287c4af90d381d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -12.338ex; width:46.75ex; height:25.843ex;" alt="{\displaystyle {\begin{aligned}\ln(ab)=\int _{1}^{ab}{\frac {1}{x}}\,dx&=\int _{1}^{a}{\frac {1}{x}}\,dx+\int _{a}^{ab}{\frac {1}{x}}\,dx\\[5pt]&=\int _{1}^{a}{\frac {1}{x}}\,dx+\int _{1}^{b}{\frac {1}{at}}\,d(at)\\[5pt]&=\int _{1}^{a}{\frac {1}{x}}\,dx+\int _{1}^{b}{\frac {1}{t}}\,dt\\[5pt]&=\ln a+\ln b.\end{aligned}}}"></span> </p> <div class="mw-heading mw-heading2"><h2 id="Aydatn">Aydatn</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Alugaritm_agaman&veaction=edit&section=3" title="Snfl tigzmi: Aydatn" class="mw-editsection-visualeditor"><span>ssnfl</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Alugaritm_agaman&action=edit&section=3" title="Modifier le code source de la section : Aydatn"><span>Snfl asagm</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/Afaylu:Log_(2).svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Log_%282%29.svg/264px-Log_%282%29.svg.png" decoding="async" width="264" height="263" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Log_%282%29.svg/396px-Log_%282%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Log_%282%29.svg/528px-Log_%282%29.svg.png 2x" data-file-width="386" data-file-height="385" /></a><figcaption>Tasɣnt n ulugaritm agaman</figcaption></figure> <div class="mw-heading mw-heading4"><h4 id="Taɣlalt_d_tsbk_n_tasɣnt_n_ulugaritm_agaman"><span id="Ta.C9.A3lalt_d_tsbk_n_tas.C9.A3nt_n_ulugaritm_agaman"></span>Taɣlalt d tsbk n tasɣnt n ulugaritm agaman</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Alugaritm_agaman&veaction=edit&section=4" title="Snfl tigzmi: Taɣlalt d tsbk n tasɣnt n ulugaritm agaman" class="mw-editsection-visualeditor"><span>ssnfl</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Alugaritm_agaman&action=edit&section=4" title="Modifier le code source de la section : Taɣlalt d tsbk n tasɣnt n ulugaritm agaman"><span>Snfl asagm</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Zɣ aylli izrin ar nttafa mas d tasɣnt <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\mapsto ln(x)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo stretchy="false">↦</mo> <mi>l</mi> <mi>n</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x\mapsto ln(x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e80f422311fda586b83a945781cfc3346ad79816" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.171ex; height:2.843ex;" alt="{\displaystyle x\mapsto ln(x)}"></span> tlla ɣar ɣ uzilal <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 ]0;+\infty [}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">]</mo> <mn>0</mn> <mo>;</mo> <mo>+</mo> <mi mathvariant="normal">∞</mi> <mo stretchy="false">[</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ]0;+\infty [}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9a2b9afa8192cc3f8173fadddad0d1f5c499d881" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.622ex; height:2.843ex;" alt="{\displaystyle ]0;+\infty [}"></span> , nzḍar ad tt nzllm ɣ ammas n uzilal ad nit d: </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 \forall x\in \mathbb {R} _{+}^{*},\ \ln '(x)={\frac {1}{x}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∀</mi> <mi>x</mi> <mo>∈</mo> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>,</mo> <mtext> </mtext> <msup> <mi>ln</mi> <mo>′</mo> </msup> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>x</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \forall x\in \mathbb {R} _{+}^{*},\ \ln '(x)={\frac {1}{x}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b22f38d71e28054b965739d367fdb1b6b791d241" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:21.681ex; height:5.176ex;" alt="{\displaystyle \forall x\in \mathbb {R} _{+}^{*},\ \ln '(x)={\frac {1}{x}}}"></span> </p><p>S ɣikAd tilia <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"> <mi>l</mi> <mi>n</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/2234193f1d24ab0337abad752c47e059232e6fcd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.088ex; height:2.176ex;" alt="{\displaystyle ln}"></span> tasɣnt tamaɣlalt ɣ uzilal <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 ]0;+\infty [}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">]</mo> <mn>0</mn> <mo>;</mo> <mo>+</mo> <mi mathvariant="normal">∞</mi> <mo stretchy="false">[</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ]0;+\infty [}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9a2b9afa8192cc3f8173fadddad0d1f5c499d881" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.622ex; height:2.843ex;" alt="{\displaystyle ]0;+\infty [}"></span>, acku tazllumt nns tga tumnigt rad nini ma sd <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"> <mi>l</mi> <mi>n</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/2234193f1d24ab0337abad752c47e059232e6fcd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.088ex; height:2.176ex;" alt="{\displaystyle ln}"></span> tga tasɣnt igmmn ɣ ammas uzilal <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 ]0;+\infty [}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">]</mo> <mn>0</mn> <mo>;</mo> <mo>+</mo> <mi mathvariant="normal">∞</mi> <mo stretchy="false">[</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ]0;+\infty [}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9a2b9afa8192cc3f8173fadddad0d1f5c499d881" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.622ex; height:2.843ex;" alt="{\displaystyle ]0;+\infty [}"></span> </p> <div class="mw-heading mw-heading4"><h4 id="Timhal_f_tasɣnt_n_ulugaritm_agaman"><span id="Timhal_f_tas.C9.A3nt_n_ulugaritm_agaman"></span>Timhal f tasɣnt n ulugaritm agaman</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Alugaritm_agaman&veaction=edit&section=5" title="Snfl tigzmi: Timhal f tasɣnt n ulugaritm agaman" class="mw-editsection-visualeditor"><span>ssnfl</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Alugaritm_agaman&action=edit&section=5" title="Modifier le code source de la section : Timhal f tasɣnt n ulugaritm agaman"><span>Snfl asagm</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Ad tg <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 f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.279ex; height:2.509ex;" alt="{\displaystyle f}"></span> yat tsɣnt <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 \ f(x)=\ln(ax)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>ln</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ f(x)=\ln(ax)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f6525fa6be559b7735674cf13fc3b57a726902a7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.405ex; height:2.843ex;" alt="{\displaystyle \ f(x)=\ln(ax)}"></span> s <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span> d <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> sin imḍann umnign. Tazllumt nns tga tazllumt nit n ulugaritm agaman, ilmma: </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 \ f(x)=\ln(x)+k\ /\ k\in \ R}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>ln</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mi>k</mi> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mtext> </mtext> <mi>k</mi> <mo>∈</mo> <mtext> </mtext> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ f(x)=\ln(x)+k\ /\ k\in \ R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/251f9da3b83fa94d8db51d4f90e012d08084e0a6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:25.947ex; height:2.843ex;" alt="{\displaystyle \ f(x)=\ln(x)+k\ /\ k\in \ R}"></span> </p><p>Acku <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="{\textstyle f(1)=k}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>=</mo> <mi>k</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle f(1)=k}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e757a34085a2f8fb3fdde644efd37258d38f0405" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.56ex; height:2.843ex;" alt="{\textstyle f(1)=k}"></span> rad nini mas d <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(a)=k}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>l</mi> <mi>n</mi> <mo stretchy="false">(</mo> <mi>a</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>k</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ln(a)=k}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/753b79806440b49757af3a855a353e7f80fdd3ff" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.437ex; height:2.843ex;" alt="{\displaystyle ln(a)=k}"></span> , s yat tɣarast igan tamatayt: </p> <ul><li><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 \forall (a;b)\in ]0:+\infty [^{2},\ \ln(ab)=\ln(a)+\ln(b)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∀</mi> <mo stretchy="false">(</mo> <mi>a</mi> <mo>;</mo> <mi>b</mi> <mo stretchy="false">)</mo> <mo>∈</mo> <mo stretchy="false">]</mo> <mn>0</mn> <mo>:</mo> <mo>+</mo> <mi mathvariant="normal">∞</mi> <msup> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>,</mo> <mtext> </mtext> <mi>ln</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mi>b</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>ln</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mi>ln</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>b</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \forall (a;b)\in ]0:+\infty [^{2},\ \ln(ab)=\ln(a)+\ln(b)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b82a9f70dc4d37520a622aa11d284072b8940537" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:41.779ex; height:3.176ex;" alt="{\displaystyle \forall (a;b)\in ]0:+\infty [^{2},\ \ln(ab)=\ln(a)+\ln(b)}"></span></li></ul> <p>Zɣ uyda yad rad naf aydatn ddaw as: </p> <ul><li><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 \forall (a;b)\in ]0:+\infty [^{2},\ \ln \left({\frac {a}{b}}\right)=\ln(a)-\ln(b)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∀</mi> <mo stretchy="false">(</mo> <mi>a</mi> <mo>;</mo> <mi>b</mi> <mo stretchy="false">)</mo> <mo>∈</mo> <mo stretchy="false">]</mo> <mn>0</mn> <mo>:</mo> <mo>+</mo> <mi mathvariant="normal">∞</mi> <msup> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>,</mo> <mtext> </mtext> <mi>ln</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>a</mi> <mi>b</mi> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mi>ln</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>ln</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>b</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \forall (a;b)\in ]0:+\infty [^{2},\ \ln \left({\frac {a}{b}}\right)=\ln(a)-\ln(b)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/be7a5b58797e75ef324c761d5000fddeb7651f6e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:42.584ex; height:5.009ex;" alt="{\displaystyle \forall (a;b)\in ]0:+\infty [^{2},\ \ln \left({\frac {a}{b}}\right)=\ln(a)-\ln(b)}"></span></li></ul> <p>Iɣ iga <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 n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> amḍan waxiḍ: </p> <ul><li><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 \forall a\in ]0;+\infty [,\ \forall n\in \mathbb {Z} ,\ \ln(a^{n})=n\ln(a)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∀</mi> <mi>a</mi> <mo>∈</mo> <mo stretchy="false">]</mo> <mn>0</mn> <mo>;</mo> <mo>+</mo> <mi mathvariant="normal">∞</mi> <mo stretchy="false">[</mo> <mo>,</mo> <mtext> </mtext> <mi mathvariant="normal">∀</mi> <mi>n</mi> <mo>∈</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mo>,</mo> <mtext> </mtext> <mi>ln</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mo stretchy="false">)</mo> <mo>=</mo> <mi>n</mi> <mi>ln</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \forall a\in ]0;+\infty [,\ \forall n\in \mathbb {Z} ,\ \ln(a^{n})=n\ln(a)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b6f04d2e3f902b8050e7c7103f83607f21f2c1b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:39.09ex; height:2.843ex;" alt="{\displaystyle \forall a\in ]0;+\infty [,\ \forall n\in \mathbb {Z} ,\ \ln(a^{n})=n\ln(a)}"></span></li> <li><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 \forall a\in ]0;+\infty [,\ \forall r\in \mathbb {Q} ,\ \ln(a^{r})=r\ln(a)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∀</mi> <mi>a</mi> <mo>∈</mo> <mo stretchy="false">]</mo> <mn>0</mn> <mo>;</mo> <mo>+</mo> <mi mathvariant="normal">∞</mi> <mo stretchy="false">[</mo> <mo>,</mo> <mtext> </mtext> <mi mathvariant="normal">∀</mi> <mi>r</mi> <mo>∈</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Q</mi> </mrow> <mo>,</mo> <mtext> </mtext> <mi>ln</mi> <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> <mi>ln</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \forall a\in ]0;+\infty [,\ \forall r\in \mathbb {Q} ,\ \ln(a^{r})=r\ln(a)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/38cef3f3f5057e91f503c68cbb07f8afc8a63d8d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:38.411ex; height:2.843ex;" alt="{\displaystyle \forall a\in ]0;+\infty [,\ \forall r\in \mathbb {Q} ,\ \ln(a^{r})=r\ln(a)}"></span></li></ul> <p>Iɣ iga <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 n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> amḍan ana: </p> <ul><li><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 \forall a\in \mathbb {R} ^{*},\ \forall \;n\in \mathbb {Z} ^{*},\ \ln(a^{n})=2n\ln |a|}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∀</mi> <mi>a</mi> <mo>∈</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> <mo>,</mo> <mtext> </mtext> <mi mathvariant="normal">∀</mi> <mspace width="thickmathspace" /> <mi>n</mi> <mo>∈</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> <mo>,</mo> <mtext> </mtext> <mi>ln</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mo stretchy="false">)</mo> <mo>=</mo> <mn>2</mn> <mi>n</mi> <mi>ln</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \forall a\in \mathbb {R} ^{*},\ \forall \;n\in \mathbb {Z} ^{*},\ \ln(a^{n})=2n\ln |a|}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9535d8f8dab30da7920e9efdee519785a7d5127b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:37.579ex; height:2.843ex;" alt="{\displaystyle \forall a\in \mathbb {R} ^{*},\ \forall \;n\in \mathbb {Z} ^{*},\ \ln(a^{n})=2n\ln |a|}"></span></li> <li><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 \forall (a_{1},a_{2},....,a_{k})\in ]0:+\infty [^{k},\ \sum _{n=1}^{k}\ln(a_{n})=\ln(\prod _{n=1}^{k}a_{n})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∀</mi> <mo stretchy="false">(</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo>∈</mo> <mo stretchy="false">]</mo> <mn>0</mn> <mo>:</mo> <mo>+</mo> <mi mathvariant="normal">∞</mi> <msup> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msup> <mo>,</mo> <mtext> </mtext> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </munderover> <mi>ln</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo>=</mo> <mi>ln</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <munderover> <mo>∏</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </munderover> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \forall (a_{1},a_{2},....,a_{k})\in ]0:+\infty [^{k},\ \sum _{n=1}^{k}\ln(a_{n})=\ln(\prod _{n=1}^{k}a_{n})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b986b1d2f8d3f8be67a75962fc87a625f45ce7ac" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:53.745ex; height:7.343ex;" alt="{\displaystyle \forall (a_{1},a_{2},....,a_{k})\in ]0:+\infty [^{k},\ \sum _{n=1}^{k}\ln(a_{n})=\ln(\prod _{n=1}^{k}a_{n})}"></span></li></ul> <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 \prod }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∏</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \prod }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a90a03f5558eba2072a554f4fc0e5c01f6b20a24" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:2.969ex; height:3.843ex;" alt="{\displaystyle \prod }"></span> ad igan tamatart n ufaris. </p> <div class="mw-heading mw-heading4"><h4 id="Aydatn_yaḍnin"><span id="Aydatn_ya.E1.B8.8Dnin"></span>Aydatn yaḍnin</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Alugaritm_agaman&veaction=edit&section=6" title="Snfl tigzmi: Aydatn yaḍnin" class="mw-editsection-visualeditor"><span>ssnfl</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Alugaritm_agaman&action=edit&section=6" title="Modifier le code source de la section : Aydatn yaḍnin"><span>Snfl asagm</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><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 1=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ln</mi> <mo>⁡</mo> <mn>1</mn> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ln 1=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b56677c77095e38669c0a4a5c7f885cee45faec2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.75ex; height:2.176ex;" alt="{\displaystyle \ln 1=0}"></span></li> <li><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 e=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ln</mi> <mo>⁡</mo> <mi>e</mi> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ln e=1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ac39a99258627c071061334973932ca14bdf0a6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.671ex; height:2.176ex;" alt="{\displaystyle \ln e=1}"></span></li> <li><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(xy)=\ln x+\ln y\quad {\text{i }}\;x>0\;{\text{d }}\;y>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ln</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mi>y</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>ln</mi> <mo>⁡</mo> <mi>x</mi> <mo>+</mo> <mi>ln</mi> <mo>⁡</mo> <mi>y</mi> <mspace width="1em" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>i </mtext> </mrow> <mspace width="thickmathspace" /> <mi>x</mi> <mo>></mo> <mn>0</mn> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>d </mtext> </mrow> <mspace width="thickmathspace" /> <mi>y</mi> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ln(xy)=\ln x+\ln y\quad {\text{i }}\;x>0\;{\text{d }}\;y>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/76c504c8a734a04d88386613875547496b23be1a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:37.677ex; height:2.843ex;" alt="{\displaystyle \ln(xy)=\ln x+\ln y\quad {\text{i }}\;x>0\;{\text{d }}\;y>0}"></span></li> <li><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^{y})=y\ln x\quad {\text{i }}\;x>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ln</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msup> <mo stretchy="false">)</mo> <mo>=</mo> <mi>y</mi> <mi>ln</mi> <mo>⁡</mo> <mi>x</mi> <mspace width="1em" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>i </mtext> </mrow> <mspace width="thickmathspace" /> <mi>x</mi> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ln(x^{y})=y\ln x\quad {\text{i }}\;x>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ed2d76dc37eb87eb691611a7f686a9cdd678d700" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:24.211ex; height:2.843ex;" alt="{\displaystyle \ln(x^{y})=y\ln x\quad {\text{i }}\;x>0}"></span></li> <li><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<\ln y\quad {\text{i }}\;0<x<y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ln</mi> <mo>⁡</mo> <mi>x</mi> <mo><</mo> <mi>ln</mi> <mo>⁡</mo> <mi>y</mi> <mspace width="1em" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>i </mtext> </mrow> <mspace width="thickmathspace" /> <mn>0</mn> <mo><</mo> <mi>x</mi> <mo><</mo> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ln x<\ln y\quad {\text{i }}\;0<x<y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ed67b4f436f8b9b9b20700fde14cd826ae0fc449" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:24.276ex; height:2.509ex;" alt="{\displaystyle \ln x<\ln y\quad {\text{i }}\;0<x<y}"></span></li> <li><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}{\frac {\ln(1+x)}{x}}=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <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> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>ln</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> <mi>x</mi> </mfrac> </mrow> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lim _{x\to 0}{\frac {\ln(1+x)}{x}}=1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/31a32ef3d5fbd5df0406c68a2ad58e415ae641d4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:17.971ex; height:5.843ex;" alt="{\displaystyle \lim _{x\to 0}{\frac {\ln(1+x)}{x}}=1}"></span></li> <li><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 _{\alpha \to 0}{\frac {x^{\alpha }-1}{\alpha }}=\ln x\quad {\text{i }}\;x>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> <mo stretchy="false">→</mo> <mn>0</mn> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msup> <mo>−</mo> <mn>1</mn> </mrow> <mi>α</mi> </mfrac> </mrow> <mo>=</mo> <mi>ln</mi> <mo>⁡</mo> <mi>x</mi> <mspace width="1em" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>i </mtext> </mrow> <mspace width="thickmathspace" /> <mi>x</mi> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lim _{\alpha \to 0}{\frac {x^{\alpha }-1}{\alpha }}=\ln x\quad {\text{i }}\;x>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8e0ed3c244443a331863809d44bf918185f18201" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:27.897ex; height:5.343ex;" alt="{\displaystyle \lim _{\alpha \to 0}{\frac {x^{\alpha }-1}{\alpha }}=\ln x\quad {\text{i }}\;x>0}"></span></li> <li><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 {x-1}{x}}\leq \ln x\leq x-1\quad {\text{i}}\quad x>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>x</mi> <mo>−</mo> <mn>1</mn> </mrow> <mi>x</mi> </mfrac> </mrow> <mo>≤</mo> <mi>ln</mi> <mo>⁡</mo> <mi>x</mi> <mo>≤</mo> <mi>x</mi> <mo>−</mo> <mn>1</mn> <mspace width="1em" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>i</mtext> </mrow> <mspace width="1em" /> <mi>x</mi> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {x-1}{x}}\leq \ln x\leq x-1\quad {\text{i}}\quad x>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/da826397d021907488f43b90e2bf8cbc04c566e5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:32.237ex; height:5.176ex;" alt="{\displaystyle {\frac {x-1}{x}}\leq \ln x\leq x-1\quad {\text{i}}\quad x>0}"></span></li> <li><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 {(1+x^{\alpha })}\leq \alpha x\quad {\text{i}}\quad x\geq 0\;{\text{d }}\;\alpha \geq 1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ln</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msup> <mo stretchy="false">)</mo> </mrow> <mo>≤</mo> <mi>α</mi> <mi>x</mi> <mspace width="1em" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>i</mtext> </mrow> <mspace width="1em" /> <mi>x</mi> <mo>≥</mo> <mn>0</mn> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>d </mtext> </mrow> <mspace width="thickmathspace" /> <mi>α</mi> <mo>≥</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ln {(1+x^{\alpha })}\leq \alpha x\quad {\text{i}}\quad x\geq 0\;{\text{d }}\;\alpha \geq 1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3bb457b7b43f802fbb8b02a4f31dbab3235d8931" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:36.463ex; height:2.843ex;" alt="{\displaystyle \ln {(1+x^{\alpha })}\leq \alpha x\quad {\text{i}}\quad x\geq 0\;{\text{d }}\;\alpha \geq 1}"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="Amawal">Amawal</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Alugaritm_agaman&veaction=edit&section=7" title="Snfl tigzmi: Amawal" class="mw-editsection-visualeditor"><span>ssnfl</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Alugaritm_agaman&action=edit&section=7" title="Modifier le code source de la section : Amawal"><span>Snfl asagm</span></a><span class="mw-editsection-bracket">]</span></span></div> <div style="column-count:4;-moz-column-count:3;-webkit-column count:"> <ul><li>Agaman : naturel</li> <li>Tasɣnt, Tawwuri : fonction</li> <li>Afaris : produit</li> <li>Timrnit : somme</li> <li>Azadur : base</li> <li>Tamnzut : fonction primitive</li> <li>Azilal : intervalle</li> <li>Amusnak : mathematicien</li> <li>Taflwit : tableau</li> <li>Tazmilt : notion</li> <li>Asnml : definition</li> <li>Anrar : aire</li> <li>Ayda : propriete</li> <li>Aɣrd : integrale</li> <li>Tafult : partie</li> <li>Amutti : variable</li> <li>Taɣlalt : continuite</li> <li>Uzdir : negatif</li> <li>Tsbk : monotonie</li> <li>Zllm : deriver</li> <li>Igmmn : croissante</li> <li>Umnig : positif</li> <li>Tamhlt : opperation</li> <li>Amḍan : nombre</li> <li>Amatay : general</li> <li>Waxiḍ : impair</li> <li>Ana : paire</li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="Isaɣuln"><span id="Isa.C9.A3uln"></span>Isaɣuln</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Alugaritm_agaman&veaction=edit&section=8" title="Snfl tigzmi: Isaɣuln" class="mw-editsection-visualeditor"><span>ssnfl</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Alugaritm_agaman&action=edit&section=8" title="Modifier le code source de la section : Isaɣuln"><span>Snfl asagm</span></a><span class="mw-editsection-bracket">]</span></span></div> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text"><a rel="nofollow" class="external free" href="https://www.britannica.com/science/logarithm">https://www.britannica.com/science/logarithm</a> <i>Encyclopedia Britannica</i>. 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Alugaritm agaman — Wikipedia