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title="Tungkol sa proyekto, ano ang maari mong gawin, at kung saan maari maghanap ng mga bagay"><span>Pamayanan</span></a></li><li id="n-Kapihan" class="mw-list-item"><a href="/wiki/Wikipedia:Kapihan"><span>Kapihan</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Natatangi:Mga_huling_binago" title="Tala ng mga huling pagbabago sa wiki. [r]" accesskey="r"><span>Mga huling binago</span></a></li><li id="n-contactpage" class="mw-list-item"><a href="/wiki/Wikipedia:Makipag-ugnayan_sa_amin" title="Paano makokontak ang Wikipedia"><span>Makipag-ugnayan</span></a></li><li id="n-help" class="mw-list-item"><a href="/wiki/Wikipedia:Tulong" title="Ang lugar para maghanap ng tulong sa Wikipedia."><span>Tulong</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Unang_Pahina" class="mw-logo"> <img class="mw-logo-icon" src="/static/images/icons/wikipedia.png" alt="" aria-hidden="true" height="50" width="50"> <span class="mw-logo-container skin-invert"> <img class="mw-logo-wordmark" alt="Wikipedia" src="/static/images/mobile/copyright/wikipedia-wordmark-en.svg" style="width: 7.5em; height: 1.125em;"> <img class="mw-logo-tagline" alt="Ang Malayang Ensiklopedya" src="/static/images/mobile/copyright/wikipedia-tagline-tl.svg" width="119" height="13" style="width: 7.4375em; height: 0.8125em;"> </span> </a> </div> <div class="vector-header-end"> <div id="p-search" role="search" class="vector-search-box-vue vector-search-box-collapses vector-search-box-show-thumbnail vector-search-box-auto-expand-width vector-search-box"> <a href="/wiki/Natatangi:Maghanap" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Maghanap sa Wikipedia [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Hanapin</span> </a> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail cdx-typeahead-search--auto-expand-width"> <form action="/w/index.php" id="searchform" class="cdx-search-input cdx-search-input--has-end-button"> <div id="simpleSearch" class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="Maghanap sa Wikipedia" aria-label="Maghanap sa Wikipedia" autocapitalize="sentences" title="Maghanap sa Wikipedia [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Natatangi:Maghanap"> </div> <button class="cdx-button cdx-search-input__end-button">Hanapin</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Mga pansariling kagamitan"> <div class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="Itsura"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Change the appearance of the page's font size, width, and color" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="Itsura" > <label id="vector-appearance-dropdown-label" for="vector-appearance-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-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">Itsura</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_tl.wikipedia.org&uselang=tl" class=""><span>Donasyon</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=Natatangi:Likhain_ang_kuwenta&returnto=Logaritmo" title="Mas maganda kung gagawa ka ng account at magla-login; gayunpaman, hindi ka pinipilit gawin ito" class=""><span>Gumawa ng account</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=Natatangi:Paglagda_ng_tagagamit&returnto=Logaritmo" title="Mas maganda kung magla-login ka; gayunpaman, hindi ka pinipilit gawin ito [o]" accesskey="o" class=""><span>Mag-login</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="Marami pang pagpipilian" > <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="Mga pansariling kagamitan" > <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">Mga pansariling kagamitan</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal" title="User menu" > <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_tl.wikipedia.org&uselang=tl"><span>Donasyon</span></a></li><li id="pt-contribute" class="mw-list-item"><a href="/wiki/Natatangi:Contribute"><span class="vector-icon mw-ui-icon-edit mw-ui-icon-wikimedia-edit"></span> <span>Mag-ambag</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Natatangi:Likhain_ang_kuwenta&returnto=Logaritmo" title="Mas maganda kung gagawa ka ng account at magla-login; gayunpaman, hindi ka pinipilit gawin ito"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Gumawa ng account</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Natatangi:Paglagda_ng_tagagamit&returnto=Logaritmo" title="Mas maganda kung magla-login ka; gayunpaman, hindi ka pinipilit gawin ito [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Mag-login</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"> Mga pahina para sa naka-logout na mga patnugot o editor <a href="/wiki/Wikipedia:Maligayang_pagdating!" aria-label="Alamin pa ang tungkol sa pagpapatnugot"><span>alamin pa</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Natatangi:Usapan_ko" title="Usapang tungkol sa mga pagbabagong ginawa sa ip address na ito [n]" accesskey="n"><span>Usapan</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> </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="Sayt"> <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="Mga nilalaman" 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">Mga nilalaman</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">ilipat sa gilid</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">itago</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">Simula</div> </a> </li> <li id="toc-Kahulugan" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Kahulugan"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Kahulugan</span> </div> </a> <ul id="toc-Kahulugan-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="Mga nilalaman" 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="Itago/Ipakita ang talaan ng mga nilalaman" > <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">Itago/Ipakita ang talaan ng mga nilalaman</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">Logaritmo</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="Pumunta sa isang artikulo na nakasulat sa ibang wika. Mayroon ito sa 109 (na) wika" > <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 (na) wika</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/Logaritme" title="Logaritme – Afrikaans" lang="af" hreflang="af" data-title="Logaritme" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" 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 – Alemannic" lang="gsw" hreflang="gsw" data-title="Logarithmus" data-language-autonym="Alemannisch" data-language-local-name="Alemannic" 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 – Amharic" lang="am" hreflang="am" data-title="ሎጋሪዝም" data-language-autonym="አማርኛ" data-language-local-name="Amharic" 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 – Aragonese" lang="an" hreflang="an" data-title="Logaritmo" data-language-autonym="Aragonés" data-language-local-name="Aragonese" 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 – Arabic" lang="ar" hreflang="ar" data-title="لوغاريتم" data-language-autonym="العربية" data-language-local-name="Arabic" 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 – Moroccan Arabic" lang="ary" hreflang="ary" data-title="لوڭاريتم" data-language-autonym="الدارجة" data-language-local-name="Moroccan Arabic" 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 – Assamese" lang="as" hreflang="as" data-title="ঘাতাংক" data-language-autonym="অসমীয়া" data-language-local-name="Assamese" 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 – Asturian" lang="ast" hreflang="ast" data-title="Logaritmu" data-language-autonym="Asturianu" data-language-local-name="Asturian" 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 – Azerbaijani" lang="az" hreflang="az" data-title="Loqarifm" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" 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 – Bashkir" lang="ba" hreflang="ba" data-title="Логарифм" data-language-autonym="Башҡортса" data-language-local-name="Bashkir" 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 – Samogitian" lang="sgs" hreflang="sgs" data-title="Luogarėtmos" data-language-autonym="Žemaitėška" data-language-local-name="Samogitian" 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 – Central Bikol" lang="bcl" hreflang="bcl" data-title="Logaritmo" data-language-autonym="Bikol Central" data-language-local-name="Central Bikol" 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 – Belarusian" lang="be" hreflang="be" data-title="Лагарыфм" data-language-autonym="Беларуская" data-language-local-name="Belarusian" 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 – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Лягарытм" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" 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 – Bulgarian" lang="bg" hreflang="bg" data-title="Логаритъм" data-language-autonym="Български" data-language-local-name="Bulgarian" 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 – Banjar" lang="bjn" hreflang="bjn" data-title="Logaritma" data-language-autonym="Banjar" data-language-local-name="Banjar" 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 – Bangla" lang="bn" hreflang="bn" data-title="লগারিদম" data-language-autonym="বাংলা" data-language-local-name="Bangla" 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 – Breton" lang="br" hreflang="br" data-title="Logaritm" 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/Logaritam" title="Logaritam – Bosnian" lang="bs" hreflang="bs" data-title="Logaritam" data-language-autonym="Bosanski" data-language-local-name="Bosnian" 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 – Russia Buriat" lang="bxr" hreflang="bxr" data-title="Логарифм" data-language-autonym="Буряад" data-language-local-name="Russia Buriat" 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 – Catalan" lang="ca" hreflang="ca" data-title="Logaritme" 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" title="لۆگاریتم – Central Kurdish" lang="ckb" hreflang="ckb" data-title="لۆگاریتم" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" 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 – Czech" lang="cs" hreflang="cs" data-title="Logaritmus" data-language-autonym="Čeština" data-language-local-name="Czech" 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 – Chuvash" lang="cv" hreflang="cv" data-title="Логарифм" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" 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 – Welsh" lang="cy" hreflang="cy" data-title="Logarithm" data-language-autonym="Cymraeg" data-language-local-name="Welsh" 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 – Danish" lang="da" hreflang="da" data-title="Logaritme" data-language-autonym="Dansk" data-language-local-name="Danish" 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 – German" lang="de" hreflang="de" data-title="Logarithmus" data-language-autonym="Deutsch" data-language-local-name="German" 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 – Zazaki" lang="diq" hreflang="diq" data-title="Logaritma" data-language-autonym="Zazaki" data-language-local-name="Zazaki" 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 – Greek" lang="el" hreflang="el" data-title="Λογάριθμος" data-language-autonym="Ελληνικά" data-language-local-name="Greek" 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 – Emiliano-Romagnolo" lang="egl" hreflang="egl" data-title="Logarìtem" data-language-autonym="Emiliàn e rumagnòl" data-language-local-name="Emiliano-Romagnolo" class="interlanguage-link-target"><span>Emiliàn e rumagnòl</span></a></li><li class="interlanguage-link interwiki-en badge-Q17437796 badge-featuredarticle mw-list-item" title="mga napiling artikulo"><a href="https://en.wikipedia.org/wiki/Logarithm" title="Logarithm – English" lang="en" hreflang="en" data-title="Logarithm" data-language-autonym="English" data-language-local-name="English" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Logaritmo" title="Logaritmo – Esperanto" lang="eo" hreflang="eo" data-title="Logaritmo" data-language-autonym="Esperanto" data-language-local-name="Esperanto" 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 – Spanish" lang="es" hreflang="es" data-title="Logaritmo" data-language-autonym="Español" data-language-local-name="Spanish" 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 – Estonian" lang="et" hreflang="et" data-title="Logaritm" data-language-autonym="Eesti" data-language-local-name="Estonian" 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 – Basque" lang="eu" hreflang="eu" data-title="Logaritmo" data-language-autonym="Euskara" data-language-local-name="Basque" 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 – Extremaduran" lang="ext" hreflang="ext" data-title="Logaritmu" data-language-autonym="Estremeñu" data-language-local-name="Extremaduran" 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 – Persian" lang="fa" hreflang="fa" data-title="لگاریتم" data-language-autonym="فارسی" data-language-local-name="Persian" 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 – Finnish" lang="fi" hreflang="fi" data-title="Logaritmi" data-language-autonym="Suomi" data-language-local-name="Finnish" 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 – Faroese" lang="fo" hreflang="fo" data-title="Logaritma" data-language-autonym="Føroyskt" data-language-local-name="Faroese" 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 – French" lang="fr" hreflang="fr" data-title="Logarithme" data-language-autonym="Français" data-language-local-name="French" 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 – Irish" lang="ga" hreflang="ga" data-title="Logartam" data-language-autonym="Gaeilge" data-language-local-name="Irish" 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 – Gan" lang="gan" hreflang="gan" data-title="對數" data-language-autonym="贛語" data-language-local-name="Gan" 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 – Guianan Creole" lang="gcr" hreflang="gcr" data-title="Logaritm" data-language-autonym="Kriyòl gwiyannen" data-language-local-name="Guianan Creole" 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 – Galician" lang="gl" hreflang="gl" data-title="Logaritmo" data-language-autonym="Galego" data-language-local-name="Galician" 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" title="לוגריתם – Hebrew" lang="he" hreflang="he" data-title="לוגריתם" data-language-autonym="עברית" data-language-local-name="Hebrew" 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%B2%E0%A4%98%E0%A5%81%E0%A4%97%E0%A4%A3%E0%A4%95" title="लघुगणक – Hindi" lang="hi" hreflang="hi" data-title="लघुगणक" data-language-autonym="हिन्दी" data-language-local-name="Hindi" 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 – Fiji Hindi" lang="hif" hreflang="hif" data-title="Logarithm" data-language-autonym="Fiji Hindi" data-language-local-name="Fiji Hindi" 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 – Croatian" lang="hr" hreflang="hr" data-title="Logaritam" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu badge-Q17437796 badge-featuredarticle mw-list-item" title="mga napiling artikulo"><a href="https://hu.wikipedia.org/wiki/Logaritmus" title="Logaritmus – Hungarian" lang="hu" hreflang="hu" data-title="Logaritmus" data-language-autonym="Magyar" data-language-local-name="Hungarian" 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 – Armenian" lang="hy" hreflang="hy" data-title="Լոգարիթմ" data-language-autonym="Հայերեն" data-language-local-name="Armenian" 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 – Interlingua" lang="ia" hreflang="ia" data-title="Logarithmo" data-language-autonym="Interlingua" data-language-local-name="Interlingua" 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 – Indonesian" lang="id" hreflang="id" data-title="Logaritma" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" 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 – Ido" lang="io" hreflang="io" data-title="Logaritmo" data-language-autonym="Ido" data-language-local-name="Ido" 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 – Icelandic" lang="is" hreflang="is" data-title="Logri" data-language-autonym="Íslenska" data-language-local-name="Icelandic" 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 – Italian" lang="it" hreflang="it" data-title="Logaritmo" data-language-autonym="Italiano" data-language-local-name="Italian" 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 – Japanese" lang="ja" hreflang="ja" data-title="対数" data-language-autonym="日本語" data-language-local-name="Japanese" 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 – Jamaican Creole English" lang="jam" hreflang="jam" data-title="Lagaridim" data-language-autonym="Patois" data-language-local-name="Jamaican Creole English" 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 – Georgian" lang="ka" hreflang="ka" data-title="ლოგარითმი" data-language-autonym="ქართული" data-language-local-name="Georgian" 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 – Kazakh" lang="kk" hreflang="kk" data-title="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/%EB%A1%9C%EA%B7%B8_(%EC%88%98%ED%95%99)" title="로그 (수학) – Korean" lang="ko" hreflang="ko" data-title="로그 (수학)" data-language-autonym="한국어" data-language-local-name="Korean" 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 – Latin" lang="la" hreflang="la" data-title="Logarithmus" data-language-autonym="Latina" data-language-local-name="Latin" 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 – Lingua Franca Nova" lang="lfn" hreflang="lfn" data-title="Logaritmo" data-language-autonym="Lingua Franca Nova" data-language-local-name="Lingua Franca Nova" 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 – Lombard" lang="lmo" hreflang="lmo" data-title="Logaritm" 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/Logaritmas" title="Logaritmas – Lithuanian" lang="lt" hreflang="lt" data-title="Logaritmas" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" 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 – Latvian" lang="lv" hreflang="lv" data-title="Logaritms" data-language-autonym="Latviešu" data-language-local-name="Latvian" 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 – Malagasy" lang="mg" hreflang="mg" data-title="Anisa" data-language-autonym="Malagasy" data-language-local-name="Malagasy" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-mk badge-Q17437796 badge-featuredarticle mw-list-item" title="mga napiling artikulo"><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 – Macedonian" lang="mk" hreflang="mk" data-title="Логаритам" data-language-autonym="Македонски" data-language-local-name="Macedonian" 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 – Malayalam" lang="ml" hreflang="ml" data-title="ലോഗരിതം" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" 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 – Marathi" lang="mr" hreflang="mr" data-title="लॉगॅरिदम" data-language-autonym="मराठी" data-language-local-name="Marathi" 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 – Malay" lang="ms" hreflang="ms" data-title="Logaritma" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" 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 – Burmese" lang="my" hreflang="my" data-title="လော့ဂရစ်သမ်" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Burmese" 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 – Low German" lang="nds" hreflang="nds" data-title="Logarithmus" data-language-autonym="Plattdüütsch" data-language-local-name="Low German" 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 – Dutch" lang="nl" hreflang="nl" data-title="Logaritme" data-language-autonym="Nederlands" data-language-local-name="Dutch" 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 – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Logaritme" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" 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 – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Logaritme" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian 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" title="Logaritme – Occitan" lang="oc" hreflang="oc" data-title="Logaritme" data-language-autonym="Occitan" data-language-local-name="Occitan" 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 – Oromo" lang="om" hreflang="om" data-title="Loogarizimii" data-language-autonym="Oromoo" data-language-local-name="Oromo" 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 – Punjabi" lang="pa" hreflang="pa" data-title="ਲਘੂਗਣਕ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" 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 – Polish" lang="pl" hreflang="pl" data-title="Logarytm" data-language-autonym="Polski" data-language-local-name="Polish" 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 – Western Punjabi" lang="pnb" hreflang="pnb" data-title="لاگرتھم" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-pt badge-Q17437796 badge-featuredarticle mw-list-item" title="mga napiling artikulo"><a href="https://pt.wikipedia.org/wiki/Logaritmo" title="Logaritmo – Portuguese" lang="pt" hreflang="pt" data-title="Logaritmo" data-language-autonym="Português" data-language-local-name="Portuguese" 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 – Romanian" lang="ro" hreflang="ro" data-title="Logaritm" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru badge-Q17437796 badge-featuredarticle mw-list-item" title="mga napiling artikulo"><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 – Russian" lang="ru" hreflang="ru" data-title="Логарифм" data-language-autonym="Русский" data-language-local-name="Russian" 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 – Yakut" lang="sah" hreflang="sah" data-title="Логарифм" data-language-autonym="Саха тыла" data-language-local-name="Yakut" 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 – Sicilian" lang="scn" hreflang="scn" data-title="Logaritmu" data-language-autonym="Sicilianu" data-language-local-name="Sicilian" 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 – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Логаритам" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" 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 – Sinhala" lang="si" hreflang="si" data-title="ලඝු ගණක" data-language-autonym="සිංහල" data-language-local-name="Sinhala" 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 – Simple English" lang="en-simple" hreflang="en-simple" data-title="Logarithm" data-language-autonym="Simple English" data-language-local-name="Simple English" 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 – Slovak" lang="sk" hreflang="sk" data-title="Logaritmus" data-language-autonym="Slovenčina" data-language-local-name="Slovak" 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 – Slovenian" lang="sl" hreflang="sl" data-title="Logaritem" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" 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 – Shona" lang="sn" hreflang="sn" data-title="Daraunene" data-language-autonym="ChiShona" data-language-local-name="Shona" 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 – Albanian" lang="sq" hreflang="sq" data-title="Logaritmet" data-language-autonym="Shqip" data-language-local-name="Albanian" 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 – Serbian" lang="sr" hreflang="sr" data-title="Логаритам" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" 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 – Swedish" lang="sv" hreflang="sv" data-title="Logaritm" data-language-autonym="Svenska" data-language-local-name="Swedish" 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 – Swahili" lang="sw" hreflang="sw" data-title="Logi" data-language-autonym="Kiswahili" data-language-local-name="Swahili" 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 – Tamil" lang="ta" hreflang="ta" data-title="மடக்கை" data-language-autonym="தமிழ்" data-language-local-name="Tamil" 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 – Thai" lang="th" hreflang="th" data-title="ลอการิทึม" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Logaritma" title="Logaritma – Turkish" lang="tr" hreflang="tr" data-title="Logaritma" data-language-autonym="Türkçe" data-language-local-name="Turkish" 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 – Tatar" lang="tt" hreflang="tt" data-title="Логарифм" data-language-autonym="Татарча / tatarça" data-language-local-name="Tatar" 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 – Ukrainian" lang="uk" hreflang="uk" data-title="Логарифм" data-language-autonym="Українська" data-language-local-name="Ukrainian" 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 – Urdu" lang="ur" hreflang="ur" data-title="لاگرتھم" data-language-autonym="اردو" data-language-local-name="Urdu" 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 – Uzbek" lang="uz" hreflang="uz" data-title="Logarifm" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi badge-Q17437796 badge-featuredarticle mw-list-item" title="mga napiling artikulo"><a href="https://vi.wikipedia.org/wiki/Logarit" title="Logarit – Vietnamese" lang="vi" hreflang="vi" data-title="Logarit" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" 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 – Waray" lang="war" hreflang="war" data-title="Logaritmo" data-language-autonym="Winaray" data-language-local-name="Waray" 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 – Wu" lang="wuu" hreflang="wuu" data-title="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-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 – Yiddish" lang="yi" hreflang="yi" data-title="לאגאריטם" data-language-autonym="ייִדיש" data-language-local-name="Yiddish" 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 – Chinese" lang="zh" hreflang="zh" data-title="对数" data-language-autonym="中文" data-language-local-name="Chinese" 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 – Minnan" lang="nan" hreflang="nan" data-title="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/%E5%B0%8D%E6%95%B8" title="對數 – Cantonese" lang="yue" hreflang="yue" data-title="對數" data-language-autonym="粵語" data-language-local-name="Cantonese" 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 href="https://www.wikidata.org/wiki/Special:EntityPage/Q11197#sitelinks-wikipedia" title="Baguhin ang link sa ibang wika" class="wbc-editpage">baguhin ang mga link</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Namespace"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Logaritmo" title="Tingnan ang nilalaman [c]" accesskey="c"><span>Artikulo</span></a></li><li id="ca-talk" class="new vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Usapan:Logaritmo&action=edit&redlink=1" rel="discussion" class="new" title="Usapan tungkol sa nilalaman nito (hindi pa naisusulat) [t]" accesskey="t"><span>Usapan</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Ibahin ang baryante o variant ng wika" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Tagalog</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Mga tingin"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Logaritmo"><span>Basahin</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Logaritmo&veaction=edit" title="Baguhin ito [v]" accesskey="v"><span>Baguhin</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Logaritmo&action=edit" title="Baguhin ang kodigong batayan ng pahinang ito [e]" accesskey="e"><span>Baguhin ang wikitext</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Logaritmo&action=history" title="Nakaraang pagbabago sa pahinang ito [h]" accesskey="h"><span>Tingnan ang kasaysayan</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Mga kagamitan" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Mga kagamitan</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Mga kagamitan</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">ilipat sa gilid</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">itago</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="More options" > <div class="vector-menu-heading"> Mga aksyon </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/Logaritmo"><span>Basahin</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Logaritmo&veaction=edit" title="Baguhin ito [v]" accesskey="v"><span>Baguhin</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Logaritmo&action=edit" title="Baguhin ang kodigong batayan ng pahinang ito [e]" accesskey="e"><span>Baguhin ang wikitext</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Logaritmo&action=history"><span>Tingnan ang kasaysayan</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Pangkalahatan </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Natatangi:Ano_ang_nakakawing_dito/Logaritmo" title="Talaan ng mga pahinang wiking nakaturo rito. [j]" accesskey="j"><span>Mga nakaturo rito</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Natatangi:Nakakawing_ng_kamakailang_pagbabago/Logaritmo" rel="nofollow" title="Mga huling binago sa mga kaugnay na pahina mula sa pahinang ito [k]" accesskey="k"><span>Kaugnay na pagbabago</span></a></li><li id="t-upload" class="mw-list-item"><a href="//commons.wikimedia.org/wiki/Special:UploadWizard?uselang=tl" title="Magkarga ng mga larawan o iba pang midya [u]" accesskey="u"><span>Mag-upload ng file</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Natatangi:Natatanging_mga_pahina" title="Tala ng mga natatanging pahina [q]" accesskey="q"><span>Natatanging pahina</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Logaritmo&oldid=1866922" title="Ibigay ang palagiang kawing para sa kasalukuyang bersyon ng pahinang ito"><span>Permanenteng link</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Logaritmo&action=info" title="More information about this page"><span>Impormasyon ng pahina</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Natatangi:Sipiin&page=Logaritmo&id=1866922&wpFormIdentifier=titleform" title="Impormasyon sa pagsangguni sa pahinang ito"><span>Sumangguni</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Natatangi:UrlShortener&url=https%3A%2F%2Ftl.wikipedia.org%2Fwiki%2FLogaritmo"><span>Kumuha ng pinaikling URL</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Natatangi:QrCode&url=https%3A%2F%2Ftl.wikipedia.org%2Fwiki%2FLogaritmo"><span>I-download ang QR code</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> I-print/I-export </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=Natatangi:Aklat&bookcmd=book_creator&referer=Logaritmo"><span>Lumikha ng isang aklat</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Natatangi:DownloadAsPdf&page=Logaritmo&action=show-download-screen"><span>I-download bilang PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Logaritmo&printable=yes" title="Ipakita ang bersyon ng pahinang itong madaling maililimbag [p]" accesskey="p"><span>Bersyong mapi-print</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"> Sa iba pang proyekto </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>Wikimedia Commons</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="Link sa nakakonektang item sa repositoryo ng datos [g]" accesskey="g"><span>Item na Wikidata</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="Page tools"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Itsura"> <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">Itsura</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">ilipat sa gilid</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">itago</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">Mula sa Wikipedia, ang malayang ensiklopedya</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-ltr mw-parser-output" lang="tl" dir="ltr"><div role="note" class="hatnote navigation-not-searchable">Huwag ikalito sa <a href="/wiki/Algoritmo" title="Algoritmo">Algoritmo</a>.</div><table class="vertical-navbox nowraplinks" style="float:right;clear:right;width:22.0em;margin:0 0 1.0em 1.0em;background:#f9f9f9;border:1px solid #aaa;padding:0.2em;border-spacing:0.4em 0;text-align:center;line-height:1.4em;font-size:88%;background-color: white; border: 1px solid #a2a9b1; border-radius: 3px;"><tbody><tr><td style="padding:0.3em 0.4em 0.3em;font-weight:bold;background-color: transparent; font-size: 150%;"> <span style="font-size:85%;">Mga <a href="/wiki/Operasyon_(matematika)" title="Operasyon (matematika)">operasyon</a> ng</span><br /><a href="/wiki/Aritmetika" title="Aritmetika">Aritmetika</a></td></tr><tr><td style="padding:0 0.1em 0.4em;font-size:108%; background-color:transparent;"> <table class="infobox" cellspacing="5" style="width: 22em; text-align: left; font-size: 88%; line-height: 1.5em; border: none; background-color: transparent;"><tbody><tr class=""><th colspan="4" style="text-align:center; font-size: 120%;"><a href="/wiki/Pagdaragdag" title="Pagdaragdag">Pagdaragdag</a> (+)</th></tr><tr class="" style=""><th style="display:none;"></th><td class="" style="text-align:right; vertical-align:middle;"><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 \scriptstyle \left.{\begin{matrix}\scriptstyle {\text{termino}}\,+\,{\text{termino}}\\\scriptstyle {\text{panagdag}}\,+\,{\text{panagdag}}\end{matrix}}\right\}\,=\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow> <mo fence="true" stretchy="true" symmetric="true"></mo> <mrow class="MJX-TeXAtom-ORD"> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mtext>termino</mtext> </mrow> <mspace width="thinmathspace" /> <mo>+</mo> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>termino</mtext> </mrow> </mstyle> </mtd> </mtr> <mtr> <mtd> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mtext>panagdag</mtext> </mrow> <mspace width="thinmathspace" /> <mo>+</mo> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>panagdag</mtext> </mrow> </mstyle> </mtd> </mtr> </mtable> </mrow> <mo>}</mo> </mrow> <mspace width="thinmathspace" /> <mo>=</mo> <mspace width="thinmathspace" /> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle \left.{\begin{matrix}\scriptstyle {\text{termino}}\,+\,{\text{termino}}\\\scriptstyle {\text{panagdag}}\,+\,{\text{panagdag}}\end{matrix}}\right\}\,=\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dab41b20d8e036ee6dbb41d82d0959a15f969839" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.702ex; margin-bottom: -0.303ex; width:19.793ex; height:4.843ex;" alt="{\displaystyle \scriptstyle \left.{\begin{matrix}\scriptstyle {\text{termino}}\,+\,{\text{termino}}\\\scriptstyle {\text{panagdag}}\,+\,{\text{panagdag}}\end{matrix}}\right\}\,=\,}"></span></td><td class="" style="text-align:left; vertical-align:middle;"><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{matrix}\scriptstyle {\text{dagup}}\\\scriptstyle {\text{suma}}\end{matrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mtext>dagup</mtext> </mrow> </mstyle> </mtd> </mtr> <mtr> <mtd> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mtext>suma</mtext> </mrow> </mstyle> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{matrix}\scriptstyle {\text{dagup}}\\\scriptstyle {\text{suma}}\end{matrix}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/957913ebe58b92fad8386e0231b472b1cc295fef" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:5.137ex; height:6.176ex;" alt="{\displaystyle {\begin{matrix}\scriptstyle {\text{dagup}}\\\scriptstyle {\text{suma}}\end{matrix}}}"></span></td><td class="" style=""></td></tr><tr class=""><th colspan="4" style="text-align:center; font-size: 120%;"><a href="/wiki/Pagbabawas" title="Pagbabawas">Pagbabawas</a> (−)</th></tr><tr class="" style=""><th style="display:none;"></th><td class="" style="text-align:right; vertical-align:middle;"><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 \scriptstyle \left.{\begin{matrix}\scriptstyle {\text{termino}}\,-\,{\text{termino}}\\\scriptstyle {\text{bawasin}}\,-\,{\text{pamawas}}\end{matrix}}\right\}\,=\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow> <mo fence="true" stretchy="true" symmetric="true"></mo> <mrow class="MJX-TeXAtom-ORD"> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mtext>termino</mtext> </mrow> <mspace width="thinmathspace" /> <mo>−</mo> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>termino</mtext> </mrow> </mstyle> </mtd> </mtr> <mtr> <mtd> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mtext>bawasin</mtext> </mrow> <mspace width="thinmathspace" /> <mo>−</mo> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>pamawas</mtext> </mrow> </mstyle> </mtd> </mtr> </mtable> </mrow> <mo>}</mo> </mrow> <mspace width="thinmathspace" /> <mo>=</mo> <mspace width="thinmathspace" /> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle \left.{\begin{matrix}\scriptstyle {\text{termino}}\,-\,{\text{termino}}\\\scriptstyle {\text{bawasin}}\,-\,{\text{pamawas}}\end{matrix}}\right\}\,=\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e38b40bbf322ba75eaf914027898a365cfcb9ab4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:18.436ex; height:4.843ex;" alt="{\displaystyle \scriptstyle \left.{\begin{matrix}\scriptstyle {\text{termino}}\,-\,{\text{termino}}\\\scriptstyle {\text{bawasin}}\,-\,{\text{pamawas}}\end{matrix}}\right\}\,=\,}"></span></td><td class="" style="text-align:left; vertical-align:middle;"><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{matrix}\scriptstyle {\text{diperensiya}}\\\scriptstyle {\text{kaibhan}}\end{matrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mtext>diperensiya</mtext> </mrow> </mstyle> </mtd> </mtr> <mtr> <mtd> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mtext>kaibhan</mtext> </mrow> </mstyle> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{matrix}\scriptstyle {\text{diperensiya}}\\\scriptstyle {\text{kaibhan}}\end{matrix}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/920e965101e90574c3d1a787899551be9f064916" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:8.851ex; height:6.176ex;" alt="{\displaystyle {\begin{matrix}\scriptstyle {\text{diperensiya}}\\\scriptstyle {\text{kaibhan}}\end{matrix}}}"></span></td><td class="" style=""></td></tr><tr class=""><th colspan="4" style="text-align:center; font-size: 120%;"><a href="/wiki/Pagpaparami_(matematika)" title="Pagpaparami (matematika)">Pagpaparami</a> (×)</th></tr><tr class="" style=""><th style="display:none;"></th><td class="" style="text-align:right; vertical-align:middle;"><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 \scriptstyle \left.{\begin{matrix}\scriptstyle {\text{kabuo}}\,\times \,{\text{kabuo}}\\\scriptstyle {\text{damihin}}\,\times \,{\text{parami}}\end{matrix}}\right\}\,=\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow> <mo fence="true" stretchy="true" symmetric="true"></mo> <mrow class="MJX-TeXAtom-ORD"> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mtext>kabuo</mtext> </mrow> <mspace width="thinmathspace" /> <mo>×</mo> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>kabuo</mtext> </mrow> </mstyle> </mtd> </mtr> <mtr> <mtd> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mtext>damihin</mtext> </mrow> <mspace width="thinmathspace" /> <mo>×</mo> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>parami</mtext> </mrow> </mstyle> </mtd> </mtr> </mtable> </mrow> <mo>}</mo> </mrow> <mspace width="thinmathspace" /> <mo>=</mo> <mspace width="thinmathspace" /> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle \left.{\begin{matrix}\scriptstyle {\text{kabuo}}\,\times \,{\text{kabuo}}\\\scriptstyle {\text{damihin}}\,\times \,{\text{parami}}\end{matrix}}\right\}\,=\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/34905602bdd1dd131005435038f7dc21f2b779c1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:16.966ex; height:4.843ex;" alt="{\displaystyle \scriptstyle \left.{\begin{matrix}\scriptstyle {\text{kabuo}}\,\times \,{\text{kabuo}}\\\scriptstyle {\text{damihin}}\,\times \,{\text{parami}}\end{matrix}}\right\}\,=\,}"></span></td><td class="" style="text-align:left; vertical-align:middle;"><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{matrix}\scriptstyle {\text{produkto}}\\\scriptstyle {\text{bunga}}\end{matrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mtext>produkto</mtext> </mrow> </mstyle> </mtd> </mtr> <mtr> <mtd> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mtext>bunga</mtext> </mrow> </mstyle> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{matrix}\scriptstyle {\text{produkto}}\\\scriptstyle {\text{bunga}}\end{matrix}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a602f4a6cc2a5e37401de593a07645637ba2da31" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:7.29ex; height:6.176ex;" alt="{\displaystyle {\begin{matrix}\scriptstyle {\text{produkto}}\\\scriptstyle {\text{bunga}}\end{matrix}}}"></span></td><td class="" style=""></td></tr><tr class=""><th colspan="4" style="text-align:center; font-size: 120%;"><a href="/wiki/Paghahati" title="Paghahati">Paghahati</a> (÷)</th></tr><tr class="" style=""><th style="display:none;"></th><td class="" style="text-align:right; vertical-align:middle;"><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 \scriptstyle \left.{\begin{matrix}\scriptstyle {\frac {\scriptstyle {\text{hatiin}}}{\scriptstyle {\text{pahati}}}}\\\scriptstyle {\text{ }}\\\scriptstyle {\frac {\scriptstyle {\text{panakda}}}{\scriptstyle {\text{pamahagi}}}}\end{matrix}}\right\}\,=\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow> <mo fence="true" stretchy="true" symmetric="true"></mo> <mrow class="MJX-TeXAtom-ORD"> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mtext>hatiin</mtext> </mrow> </mstyle> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mtext>pahati</mtext> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mtd> </mtr> <mtr> <mtd> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mtext> </mtext> </mrow> </mstyle> </mtd> </mtr> <mtr> <mtd> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mtext>panakda</mtext> </mrow> </mstyle> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mtext>pamahagi</mtext> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mtd> </mtr> </mtable> </mrow> <mo>}</mo> </mrow> <mspace width="thinmathspace" /> <mo>=</mo> <mspace width="thinmathspace" /> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle \left.{\begin{matrix}\scriptstyle {\frac {\scriptstyle {\text{hatiin}}}{\scriptstyle {\text{pahati}}}}\\\scriptstyle {\text{ }}\\\scriptstyle {\frac {\scriptstyle {\text{panakda}}}{\scriptstyle {\text{pamahagi}}}}\end{matrix}}\right\}\,=\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/adffd543decf09f38acefd67daf48678facfc801" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -5.03ex; margin-bottom: -0.308ex; width:12.043ex; height:11.509ex;" alt="{\displaystyle \scriptstyle \left.{\begin{matrix}\scriptstyle {\frac {\scriptstyle {\text{hatiin}}}{\scriptstyle {\text{pahati}}}}\\\scriptstyle {\text{ }}\\\scriptstyle {\frac {\scriptstyle {\text{panakda}}}{\scriptstyle {\text{pamahagi}}}}\end{matrix}}\right\}\,=\,}"></span></td><td class="" style="text-align:left; vertical-align:middle;"><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{matrix}\scriptstyle {\text{hatimbilang}}\\\scriptstyle {\text{kosyente}}\\\scriptstyle {\text{kahatian}}\\\scriptstyle {\text{tagway}}\end{matrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mtext>hatimbilang</mtext> </mrow> </mstyle> </mtd> </mtr> <mtr> <mtd> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mtext>kosyente</mtext> </mrow> </mstyle> </mtd> </mtr> <mtr> <mtd> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mtext>kahatian</mtext> </mrow> </mstyle> </mtd> </mtr> <mtr> <mtd> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mtext>tagway</mtext> </mrow> </mstyle> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{matrix}\scriptstyle {\text{hatimbilang}}\\\scriptstyle {\text{kosyente}}\\\scriptstyle {\text{kahatian}}\\\scriptstyle {\text{tagway}}\end{matrix}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a1febb110a5041082c46cb9035776e5ac52da997" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -5.671ex; width:9.34ex; height:12.509ex;" alt="{\displaystyle {\begin{matrix}\scriptstyle {\text{hatimbilang}}\\\scriptstyle {\text{kosyente}}\\\scriptstyle {\text{kahatian}}\\\scriptstyle {\text{tagway}}\end{matrix}}}"></span></td><td class="" style=""><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{matrix}\scriptstyle {\text{ }}\\\scriptstyle {\text{ }}\\\scriptstyle {\text{butal}}\\\scriptstyle {\text{ }}\\\scriptstyle {\text{ }}\end{matrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mtext> </mtext> </mrow> </mstyle> </mtd> </mtr> <mtr> <mtd> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mtext> </mtext> </mrow> </mstyle> </mtd> </mtr> <mtr> <mtd> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mtext>butal</mtext> </mrow> </mstyle> </mtd> </mtr> <mtr> <mtd> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mtext> </mtext> </mrow> </mstyle> </mtd> </mtr> <mtr> <mtd> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mtext> </mtext> </mrow> </mstyle> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{matrix}\scriptstyle {\text{ }}\\\scriptstyle {\text{ }}\\\scriptstyle {\text{butal}}\\\scriptstyle {\text{ }}\\\scriptstyle {\text{ }}\end{matrix}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f20775ddd2ee6f7d37085ca8c17de63b7e4f987a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -7.338ex; width:4.498ex; height:15.843ex;" alt="{\displaystyle {\begin{matrix}\scriptstyle {\text{ }}\\\scriptstyle {\text{ }}\\\scriptstyle {\text{butal}}\\\scriptstyle {\text{ }}\\\scriptstyle {\text{ }}\end{matrix}}}"></span></td></tr><tr class=""><th colspan="4" style="text-align:center; font-size: 120%;"><a href="/wiki/Pagpapalakas_(matematika)" title="Pagpapalakas (matematika)">Pagpapalakas</a></th></tr><tr class="" style=""><th style="display:none;"></th><td class="" style="text-align:right; vertical-align:middle;"><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 \scriptstyle {\text{base}}^{\text{eksponente}}\,=\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mtext>base</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>eksponente</mtext> </mrow> </msup> <mspace width="thinmathspace" /> <mo>=</mo> <mspace width="thinmathspace" /> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {\text{base}}^{\text{eksponente}}\,=\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ba6a4f582aa8ea83f05dca3767dd859493719b39" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:11.752ex; height:2.176ex;" alt="{\displaystyle \scriptstyle {\text{base}}^{\text{eksponente}}\,=\,}"></span></td><td class="" style="text-align:left; vertical-align:middle;"><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 \scriptstyle {\text{lakas}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mtext>lakas</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {\text{lakas}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/436d25b2ba0840504304f3bc79b7074b858c4a9f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.617ex; height:1.676ex;" alt="{\displaystyle \scriptstyle {\text{lakas}}}"></span></td><td class="" style=""></td></tr><tr class=""><th colspan="4" style="text-align:center; font-size: 120%;"><a href="/wiki/Ugat_(matematika)" title="Ugat (matematika)">Ugat</a> (√)</th></tr><tr class="" style=""><th style="display:none;"></th><td class="" style="text-align:right; vertical-align:middle;"><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 \scriptstyle {\sqrt[{\text{antas}}]{\scriptstyle {\text{radikando}}}}\,=\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mroot> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mtext>radikando</mtext> </mrow> </mstyle> <mrow class="MJX-TeXAtom-ORD"> <mtext>antas</mtext> </mrow> </mroot> </mrow> <mspace width="thinmathspace" /> <mo>=</mo> <mspace width="thinmathspace" /> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {\sqrt[{\text{antas}}]{\scriptstyle {\text{radikando}}}}\,=\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47dac94b774ac588a64824c33613709726d4e698" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:12.785ex; height:2.509ex;" alt="{\displaystyle \scriptstyle {\sqrt[{\text{antas}}]{\scriptstyle {\text{radikando}}}}\,=\,}"></span></td><td class="" style="text-align:left; vertical-align:middle;"><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 \scriptstyle {\text{ugat}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mtext>ugat</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {\text{ugat}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/57a45fa6334e6cce36b32fbce9bd58f33494ac5e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.198ex; height:2.009ex;" alt="{\displaystyle \scriptstyle {\text{ugat}}}"></span></td><td class="" style=""></td></tr><tr class=""><th colspan="4" style="text-align:center; font-size: 120%;"><a class="mw-selflink selflink">Logaritmo</a> (log)</th></tr><tr class="" style=""><th style="display:none;"></th><td class="" style="text-align:right; vertical-align:middle;"><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 \scriptstyle \log _{\text{base}}({\text{lakas}})\,=\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>base</mtext> </mrow> </msub> <mo>⁡</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>lakas</mtext> </mrow> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mo>=</mo> <mspace width="thinmathspace" /> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle \log _{\text{base}}({\text{lakas}})\,=\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9f8f31fb66846e8a6cc192996ec00438d006fcb5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.743ex; height:2.176ex;" alt="{\displaystyle \scriptstyle \log _{\text{base}}({\text{lakas}})\,=\,}"></span></td><td class="" style="text-align:left; vertical-align:middle;"><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 \scriptstyle {\text{logaritmo}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mrow class="MJX-TeXAtom-ORD"> <mtext>logaritmo</mtext> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle {\text{logaritmo}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e205ea765745d44755ddd8661b2117ccb4a61578" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.856ex; height:2.009ex;" alt="{\displaystyle \scriptstyle {\text{logaritmo}}}"></span></td><td class="" style=""></td></tr> </tbody></table></td> </tr><tr><td style="text-align:right;font-size:115%"><style data-mw-deduplicate="TemplateStyles:r1843287">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}.mw-parser-output .infobox .navbar{font-size:100%}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-tingnan"><a href="/wiki/Padron:Sidebar" title="Padron:Sidebar"><abbr title="Tingnan ang padron">t</abbr></a></li><li class="nv-usapan"><a href="/w/index.php?title=Usapang_padron:Sidebar&action=edit&redlink=1" class="new" title="Usapang padron:Sidebar (hindi pa naisusulat)"><abbr title="Pag-usapan ang padron">u</abbr></a></li><li class="nv-baguhin"><a class="external text" href="https://tl.wikipedia.org/w/index.php?title=Padron:Sidebar&action=edit"><abbr title="Baguhin ang padron">b</abbr></a></li></ul></div></td></tr></tbody></table><p>Sa <a href="/wiki/Matematika" title="Matematika">matematika</a>, ang <b>logaritmo</b> (mula Kastila <i>logaritmo</i>) ng isang positibong <a href="/wiki/Tunay_na_bilang" title="Tunay na bilang">tunay na bilang</a> na <i>n</i> na may báseng <i>b</i> ay ang eksponente <i>x</i> ng <i>b</i> para magresulta sa <i>n</i>. Kabaligtaran ito ng <a href="/wiki/Pagpapalakas_(matematika)" title="Pagpapalakas (matematika)">pagpapalakas</a>. </p><p><span class="nowrap">    </span><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}n=x\quad \Leftrightarrow \quad b^{x}=n}"> <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>n</mi> <mo>=</mo> <mi>x</mi> <mspace width="1em" /> <mo stretchy="false">⇔</mo> <mspace width="1em" /> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msup> <mo>=</mo> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \log _{b}n=x\quad \Leftrightarrow \quad b^{x}=n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7961a702f617bc5ffad1fb10ba67547fd93a6b7b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:25.042ex; height:2.843ex;" alt="{\displaystyle \log _{b}n=x\quad \Leftrightarrow \quad b^{x}=n}"></span> </p><p>Isinusulat ang mga logaritmo na may partikular na báse sa anyong <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}(x)}"> <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> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \log _{b}(x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8cad5f91f24392d04f1c9324d7154401e1ce3bca" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.048ex; height:2.843ex;" alt="{\displaystyle \log _{b}(x)}"></span>, kung saan ang <i>b</i> ay isinusulat nang nakababa (<i>subscript</i>). Hindi kinakailangan ang <a href="/wiki/Panaklong" title="Panaklong">panaklong</a>, bagamat ginagamit ito para magbigay-linaw. Kung tukoy na ang báse o di kaya'y hindi kailangan o maikakalito (tulad ng karaniwang logaritmo, <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"> <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/1e1be2659542850a5a4def5da1ca2bb402fbb4e6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.848ex; height:2.676ex;" alt="{\displaystyle \log _{10}}"></span>), hindi na isinusulat ang báse nito. </p><p>Unang ipinakilala ni <a href="/wiki/John_Napier" title="John Napier">John Napier</a> noong 1614 ang mga logaritmo bilang isang mas madali at mabilis na paraan sa pagkakalkula. Matapos nito, mabilis ding ginamit ito ng mga nasa larangan— nabigador, siyentipiko, inhinyero, at iba pa, gamit ng mga slide rule at talahanayan ng logaritmo. Posible ito dahil sa pagkakatuklas ng mga logaritmikong pagtutulad (<i>logarithmic identities</i>): na ang logaritmo ng isang produkto ay ang dagup (suma) ng mga logaritmo ng kabuo nito: </p><p><span class="nowrap">    </span><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}(xy)=\log _{b}(x)+\log _{b}(y)}"> <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> <mo stretchy="false">(</mo> <mi>x</mi> <mi>y</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>+</mo> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>y</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \log _{b}(xy)=\log _{b}(x)+\log _{b}(y)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a72b4b7ba4c487ba5c15587d2eff610355605901" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:28.065ex; height:2.843ex;" alt="{\displaystyle \log _{b}(xy)=\log _{b}(x)+\log _{b}(y)}"></span> </p><p>Galing kay <a href="/wiki/Leonhard_Euler" title="Leonhard Euler">Leonhard Euler</a> ang modernong pagpapakahulugan sa mga logaritmo. Itinulad niya ang mga ito sa mga <a href="/w/index.php?title=Buning_nagpapalakas&action=edit&redlink=1" class="new" title="Buning nagpapalakas (hindi pa naisusulat)">buning nagpapalakas</a> (<i>exponential functions</i>) noong ika-18 siglo. </p><p>Maraming gamit ang mga logaritmo sa iba't ibang mga larangan. Ang yunit ng <a href="/wiki/Tunog" title="Tunog">tunog</a>, <a href="/w/index.php?title=Desibel&action=edit&redlink=1" class="new" title="Desibel (hindi pa naisusulat)">desibel</a> (dB), ay ipinapakita gamit ng mga logaritmo. Ang <a href="/wiki/PH" title="PH">sukatang pH</a> ay gumagamit rin ng mga logaritmo para masukat ang kaasiman (<i>acidity</i>) ng isang bagay. May mga gamit rin ito sa <a href="/wiki/Tugtugin" title="Tugtugin">musika</a> at <a href="/wiki/Kriptograpiya" title="Kriptograpiya">kriptograpiya</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Kahulugan">Kahulugan</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Logaritmo&veaction=edit&section=1" title="Baguhin seksiyon: Kahulugan" class="mw-editsection-visualeditor"><span>baguhin</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Logaritmo&action=edit&section=1" title="Edit section's source code: Kahulugan"><span>baguhin ang wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <div role="note" class="hatnote navigation-not-searchable">Tingnan din: <a href="/wiki/Pagpapalakas_(matematika)" title="Pagpapalakas (matematika)">Pagpapalakas (matematika)</a></div> <p>Ang logaritmo ay ang kabaligtaran ng <a href="/wiki/Pagpapalakas_(matematika)" title="Pagpapalakas (matematika)">pagpapalakas</a>. Ibig sabihin, ang logaritmo ng isang positibong tunay na bilang na <i>x</i> sa may báseng <i>b</i> ay ang eksponenteng kakailanganin ng <i>b</i> para magresulta sa <i>x</i>. Sa madaling salita, ang logaritmo ng <i>x</i> sa may báseng <i>b</i> ay ang <i>y</i> sa <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"> <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/7b51b8dcca3e64714e2f3aba12bb8c68812f77cc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.475ex; height:2.343ex;" alt="{\displaystyle b^{y}=x}"></span>. </p><p>Sinusulat ito sa anyong <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}(x)}"> <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> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \log _{b}(x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8cad5f91f24392d04f1c9324d7154401e1ce3bca" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.048ex; height:2.843ex;" alt="{\displaystyle \log _{b}(x)}"></span> (binabasang "<i>ang logaritmo ng x sa báseng b</i>" o "<i>ang ika-b na base ng logaritmo ng x</i>", o di kaya, kung literal na babasahin, "<i>ang log b ng x</i>"). </p><p>Para maging posible ang kahulugan, hindi lahat ng bilang ay maaaring gamitin bilang báse nito. Kinakailangang positibo ang <i>b</i> at hindi 1 (<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"> <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/94436473a90bd55191a79c59474cb5456dcbec00" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.258ex; height:2.176ex;" alt="{\displaystyle b>0}"></span> at <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\neq 1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> <mo>≠</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b\neq 1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/32a55c3a4b8eca743088b70c7c4d63c773f43c2b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.258ex; height:2.676ex;" alt="{\displaystyle b\neq 1}"></span>). Kailangan ding positibo ang <i>x</i> (<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>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/80d24be5f0eb4a9173da6038badc8659546021d0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.591ex; height:2.176ex;" alt="{\displaystyle x>0}"></span>). Ang resulta nito ay isang tunay na bilang. </p><p><span typeof="mw:File"><a href="/wiki/Talaksan:Arithmetic_symbols.svg" class="mw-file-description" title="Matematika"><img alt="Matematika" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a3/Arithmetic_symbols.svg/35px-Arithmetic_symbols.svg.png" decoding="async" width="35" height="35" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a3/Arithmetic_symbols.svg/53px-Arithmetic_symbols.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a3/Arithmetic_symbols.svg/70px-Arithmetic_symbols.svg.png 2x" data-file-width="210" data-file-height="210" /></a></span> <i>Ang lathalaing ito na tungkol sa <b>Matematika</b> ay isang <a href="/wiki/Wikipedia:Usbong" title="Wikipedia:Usbong">usbong</a>. Makatutulong ka sa <a href="/wiki/Wikipedia" title="Wikipedia">Wikipedia</a> sa <span class="plainlinks"><a class="external text" href="https://tl.wikipedia.org/w/index.php?title=Logaritmo&action=edit">pagpapalawig</a></span> nito.</i> </p>    </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="">Kinuha sa "<a dir="ltr" href="https://tl.wikipedia.org/w/index.php?title=Logaritmo&oldid=1866922">https://tl.wikipedia.org/w/index.php?title=Logaritmo&oldid=1866922</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Natatangi:Mga_kategorya" title="Natatangi:Mga kategorya">Kategorya</a>: <ul><li><a href="/wiki/Kategorya:Mga_punsiyon_at_pagmamapa" title="Kategorya:Mga punsiyon at pagmamapa">Mga punsiyon at pagmamapa</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Nakatagong kategorya: <ul><li><a href="/wiki/Kategorya:Stub_(Matematika)" title="Kategorya:Stub (Matematika)">Stub (Matematika)</a></li><li><a href="/wiki/Kategorya:Mga_lathalaing_dapat_palawigin" title="Kategorya:Mga lathalaing dapat palawigin">Mga lathalaing dapat palawigin</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Huling pagbabago: 18:08, 17 Hunyo 2021.</li> <li id="footer-info-copyright">Magagamit ang teksto sa ilalim ng <a rel="nofollow" class="external text" href="//creativecommons.org/licenses/by-sa/4.0/">Lisensyang Creative Commons Attribution/Share-Alike</a>; maaaring mailapat ang karagdagang termino. 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