{"id":4005,"date":"2026-10-14T22:50:09","date_gmt":"2026-10-14T21:50:09","guid":{"rendered":"https:\/\/wpcalc.com\/tr\/matematik\/logaritma-hesaplama\/"},"modified":"2026-10-14T22:50:09","modified_gmt":"2026-10-14T21:50:09","slug":"logaritma-hesaplama","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/tr\/matematik\/logaritma-hesaplama\/","title":{"rendered":"Logaritma Hesaplama"},"content":{"rendered":"<section class=\"not-prose calculator-box\" aria-labelledby=\"calculator-title\"><div class=\"flex items-baseline sm:items-center justify-between gap-2 sm:gap-3\"><div class=\"flex flex-col sm:flex-row sm:items-center gap-2\"><span class=\"icon icon-calculator text-primary-700! text-base! dark:text-primary-300!\" aria-hidden=\"true\"><\/span><h2 id=\"calculator-title\" class=\"text-lg font-display font-bold\">Herhangi bir tabana g\u00f6re logaritma hesaplama<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"4005\" data-favorite-title=\"Logaritma\" data-favorite-url=\"https:\/\/wpcalc.com\/tr\/matematik\/logaritma-hesaplama\/\" data-favorite-excerpt=\"Herhangi bir pozitif say\u0131n\u0131n logaritmas\u0131n\u0131 istedi\u011finiz tabanda hesaplay\u0131n \u2014 2, 10, e (do\u011fal logaritma) veya \u00f6zel bir taban. Say\u0131y\u0131 girin, taban\u0131 se\u00e7in; sonu\u00e7la birlikte do\u011frulama ve kar\u015f\u0131la\u015ft\u0131rma i\u00e7in ortak, do\u011fal ve ikili logaritma de\u011ferlerini g\u00f6r\u00fcn.\" aria-label=\"Favorilere ekle\" data-favorite-icon=\"icon icon-algebra\">\n    <span class=\"icon icon-shape-star-empty\" aria-hidden=\"true\"><\/span>\n  <\/button>\n  <div class=\"calcdash-favorite__tip\" aria-hidden=\"true\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n  <span class=\"sr-only\" role=\"status\" id=\"favorite-status\"><\/span>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/tr\/matematik\/logaritma-hesaplama\/\" method=\"POST\" class=\"calculator\" id=\"calculator-4005\" data-post=\"4005\"><fieldset class=\"fieldset-input is-1\"><legend class=\"sr-only\">Giri\u015f alanlar\u0131<\/legend><div class=\"is-single field\" id=\"input-1\"><span class=\"font-semibold\">Say\u0131 ve taban<\/span><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-2\">Say\u0131 (x)<\/label><div class=\"term\">x<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"say_x\" id=\"field-2\" aria-describedby=\"calc-info-2\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 1000\" min=\"0\" value=\"1000\"\/><small id=\"calc-info-2\">Logaritmas\u0131 al\u0131nacak say\u0131. Pozitif olmal\u0131d\u0131r.<\/small><\/div><div class=\"field\" id=\"input-3\"><label for=\"field-3\">Taban (b)<\/label><div class=\"grid grid-cols-1\"><select id=\"field-3\" name=\"taban_b\"><option value=\"2\" selected>2 \u2014 ikili logaritma (log\u2082)<\/option><option value=\"10\">10 \u2014 onluk logaritma (log\u2081\u2080)<\/option><option value=\"e\">e \u2248 2,71828 \u2014 do\u011fal logaritma (ln)<\/option><option value=\"custom\">\u00d6zel taban\u2026<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><div class=\"field is-single\" id=\"input-4\" hidden><label for=\"field-4\">\u00d6zel taban<\/label><input type=\"text\" name=\"zel_taban\" id=\"field-4\" aria-describedby=\"calc-info-4\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 5\" min=\"0\" value=\"5\"\/><small id=\"calc-info-4\">1&#039;den farkl\u0131 pozitif bir say\u0131 (\u00f6rn. 3, 5, 2,5).<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Yeniden hesapla\" id=\"calculate-button\" data-post=\"4005\">Hesapla<\/button><button type=\"reset\">S\u0131f\u0131rla<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Otomatik hesapla<\/label><small>Etkinle\u015ftirilirse, herhangi bir de\u011feri de\u011fi\u015ftirdi\u011finizde sonu\u00e7 otomatik olarak g\u00fcncellenir.<\/small><\/div><div class=\"fieldset-result is-hidden\" aria-labelledby=\"result-title\" aria-live=\"polite\" role=\"region\"> <h3 class=\"result-title bg-gradient-to-r from-primary-50 to-gray-50 dark:from-primary-900 dark:to-gray-800\" id=\"result-title\"><span class=\"icon icon-s-pulse\" aria-hidden=\"true\"><\/span> Logaritma sonu\u00e7lar\u0131<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Logaritma log\u2091(x)<\/span><span class=\"result-term\">log\u2091(x)<\/span><\/span><span class=\"field-value\" id=\"result-1\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-2\"><span class=\"field-title\"><span>Kontrol: b \u00fczeri sonu\u00e7<\/span><\/span><span class=\"field-value\" id=\"result-2\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-3\"><span class=\"field-title\"><span>Onluk logaritma log\u2081\u2080(x)<\/span><span class=\"result-term\">log\u2081\u2080<\/span><\/span><span class=\"field-value\" id=\"result-3\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-4\"><span class=\"field-title\"><span>Do\u011fal logaritma ln(x)<\/span><span class=\"result-term\">ln<\/span><\/span><span class=\"field-value\" id=\"result-4\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-5\"><span class=\"field-title\"><span>\u0130kili logaritma log\u2082(x)<\/span><span class=\"result-term\">log\u2082<\/span><\/span><span class=\"field-value\" id=\"result-5\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-6\"><span class=\"field-title\"><span>Nas\u0131l hesapland\u0131<\/span><\/span><span class=\"field-value\" id=\"result-6\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><\/div><div class=\"result-actions\"><button type=\"button\" class=\"copy-link\"><svg viewBox=\"0 0 20 20\" fill=\"currentColor\" aria-hidden=\"true\"><path d=\"M12.232 4.232a2.5 2.5 0 0 1 3.536 3.536l-1.225 1.224a.75.75 0 0 0 1.061 1.06l1.224-1.224a4 4 0 0 0-5.656-5.656l-3 3a4 4 0 0 0 .225 5.865.75.75 0 0 0 .977-1.138 2.5 2.5 0 0 1-.142-3.667l3-3Z\"\/><path d=\"M11.603 7.963a.75.75 0 0 0-.977 1.138 2.5 2.5 0 0 1 .142 3.667l-3 3a2.5 2.5 0 0 1-3.536-3.536l1.225-1.224a.75.75 0 0 0-1.061-1.06l-1.224 1.224a4 4 0 1 0 5.656 5.656l3-3a4 4 0 0 0-.225-5.865Z\"\/><\/svg><span class=\"copy-link__text\">Bu hesaplaman\u0131n ba\u011flant\u0131s\u0131n\u0131 kopyala<\/span><\/button><span class=\"sr-only\" role=\"status\" id=\"copy-link-status\"><\/span><\/div><\/div><a href=\"#respond\" class=\"hidden transition-opacity duration-300 opacity-0 w-50 text-sm justify-center items-center gap-2 px-4 py-2 rounded bg-gray-200 text-gray-700 hover:bg-gray-300\" id=\"leave-comment\"><span class=\"icon icon-comments\" aria-hidden=\"true\"><\/span>Yorum b\u0131rak<\/a><\/form><\/section><section id=\"calc-reactions\" class=\"not-prose hidden my-12 bg-gradient-to-r from-primary-50 to-gray-50 border border-indigo-100 rounded-xl px-6 py-4 shadow-sm\" data-post=\"4005\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">Bu sonu\u00e7 hakk\u0131nda ne d\u00fc\u015f\u00fcn\u00fcyorsunuz?<\/p><div role=\"group\" aria-labelledby=\"calc-reactions-title\" class=\"grid grid-cols-3 sm:flex sm:flex-row sm:justify-around gap-4 sm:items-center sm:flex-wrap\"><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"like\"><span class=\"reaction-count\" data-reaction-count=\"like\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">Be\u011fendim <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"helpful\"><span class=\"reaction-count\" data-reaction-count=\"helpful\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\udca1 <\/span><span class=\"reaction-description font-medium\">Faydal\u0131 <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"confused\"><span class=\"reaction-count\" data-reaction-count=\"confused\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude15 <\/span><span class=\"reaction-description font-medium\">Kafam kar\u0131\u015ft\u0131 <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"disappointed\"><span class=\"reaction-count\" data-reaction-count=\"disappointed\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude1e <\/span><span class=\"reaction-description font-medium\">Hayal k\u0131r\u0131kl\u0131\u011f\u0131 <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"inaccurate\"><span class=\"reaction-count\" data-reaction-count=\"inaccurate\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\u274c <\/span><span class=\"reaction-description font-medium\">Hatal\u0131 <\/span><\/button><\/div><div id=\"reaction-message\" class=\"hidden mt-8 rounded-md border border-primary-100 bg-white\/50 backdrop-blur-sm px-4 py-2 text-sm text-center shadow-sm\"><\/div><\/section><div class=\"calcdash-ad not-prose calcdash-ad--calc_result calcdash-ad--in-article\"><ins class=\"adsbygoogle\" style=\"display:block\" data-ad-client=\"ca-pub-1721569815777345\" data-ad-slot=\"6317458308\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\"><\/ins><script>(adsbygoogle = window.adsbygoogle || []).push({});<\/script><\/div>\n<style id=\"wpcoderpro-inline-1\">.formula-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section class=\"formula-box\" aria-labelledby=\"formula-title\">\r\n\t<div id=\"formula-title\" class=\"not-prose font-display mb-4\"><span class=\"icon icon-formula\" aria-hidden=\"true\"><\/span><h2>Logaritma Form\u00fcl\u00fc<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Form\u00fcl<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\n\\[ \\log_b(x) = \\frac{\\ln(x)}{\\ln(b)} \\]\n\\[ \\text{burada } b^{\\,\\log_b(x)} = x \\]<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong> Burada:<\/strong><\/p>\n<ul>\n<li>\\(x\\) \u2014 logaritmas\u0131 hesaplanacak say\u0131; pozitif olmal\u0131d\u0131r (\\(x &gt; 0\\))<\/li>\n<li>\\(b\\) \u2014 logaritman\u0131n taban\u0131; pozitif ve 1'den farkl\u0131 olmal\u0131d\u0131r (\\(b &gt; 0,\\ b \\neq 1\\))<\/li>\n<li>\\(\\ln\\) \u2014 do\u011fal logaritma (taban\u0131 \\(e \\approx 2.71828\\) olan logaritma)<\/li>\n<\/ul>\n<p>\\(\\log_b(x)\\) logaritmas\u0131 \u015fu soruya cevap verir: \\(x\\) say\u0131s\u0131n\u0131 elde etmek i\u00e7in \\(b\\) taban\u0131 ka\u00e7\u0131nc\u0131 kuvvete y\u00fckseltilmelidir? Yukar\u0131daki taban de\u011fi\u015ftirme form\u00fcl\u00fc sayesinde herhangi bir tabandaki logaritma, do\u011fal logaritmalar kullan\u0131larak hesaplanabilir; bu hesaplay\u0131c\u0131 da yaln\u0131zca 10 ve \\(e\\) i\u00e7in de\u011fil, t\u00fcm tabanlar i\u00e7in tam olarak bu y\u00f6ntemi kullan\u0131r.<\/p>\n<p>\r\n<\/section>\n<style id=\"wpcoderpro-inline-2\">.calculation-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section id=\"calculation\" class=\"calculation-box\" aria-labelledby=\"calculation-title\">\r\n\t<div id=\"calculation-title\" class=\"not-prose font-display\"><span class=\"icon icon-unordered-list\" aria-hidden=\"true\"><\/span><h2>Logaritma \u2013 Hesaplama \u00d6rne\u011fi<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>\u00d6rnek:<\/strong> \\(\\log_2(1000)\\) de\u011ferini bulal\u0131m \u2014 yani 1000'e ula\u015fmak i\u00e7in 2 ka\u00e7\u0131nc\u0131 kuvvete y\u00fckseltilmelidir?<\/p>\n<p>\\[ \\log_2(1000) = \\frac{\\ln(1000)}{\\ln(2)} = \\frac{6.907755}{0.693147} \\]<\/p>\n<p>\\[ \\log_2(1000) \\approx 9.965784 \\]<\/p>\n<p><strong>Sonu\u00e7:<\/strong> \\(\\log_2(1000) \\approx 9.965784\\). Kontrol: \\(2^{9.965784} \\approx 1000\\), yani orijinal say\u0131 geri elde edilir.<\/p>\n<p>\n\r\n<\/section>\n<h2>Hesaplay\u0131c\u0131 Nas\u0131l Kullan\u0131l\u0131r?<\/h2>\n<ol>\n<li><strong>Say\u0131 (x)<\/strong> alan\u0131na \\(x\\) de\u011ferini girin \u2014 \u00f6rne\u011fin 1000. Say\u0131 pozitif olmal\u0131d\u0131r.<\/li>\n<li><strong>Taban (b)<\/strong> a\u00e7\u0131l\u0131r men\u00fcs\u00fcnden bir taban se\u00e7in: ikili logaritma i\u00e7in <strong>2<\/strong>, ortak logaritma i\u00e7in <strong>10<\/strong>, do\u011fal logaritma i\u00e7in <strong>e<\/strong> ya da <strong>\u00d6zel taban\u2026<\/strong>.<\/li>\n<li>\u00d6zel taban se\u00e7tiyseniz a\u00e7\u0131lan <strong>\u00d6zel taban<\/strong> alan\u0131na taban\u0131 yaz\u0131n \u2014 1'den farkl\u0131 herhangi bir pozitif say\u0131, \u00f6rne\u011fin 3, 5 veya 2,5.<\/li>\n<li>Ana sonucu <strong>Logaritma log\u2091(x)<\/strong> alan\u0131ndan okuyun, ard\u0131ndan <strong>Kontrol: b \u00fczeri sonu\u00e7<\/strong> de\u011feriyle do\u011frulay\u0131n; bu de\u011fer orijinal say\u0131n\u0131z\u0131 geri vermelidir.<\/li>\n<li>Kar\u015f\u0131la\u015ft\u0131rma i\u00e7in hesaplay\u0131c\u0131 ayr\u0131ca ortak logaritma \\(\\log_{10}(x)\\), do\u011fal logaritma \\(\\ln(x)\\) ve ikili logaritma \\(\\log_2(x)\\) de\u011ferlerini g\u00f6sterir; <strong>Nas\u0131l hesapland\u0131<\/strong> ba\u015fl\u0131\u011f\u0131 alt\u0131nda ad\u0131m ad\u0131m a\u00e7\u0131klama da yer al\u0131r.<\/li>\n<\/ol>\n<h2>Logaritma Nedir?<\/h2>\n<p>Logaritma, kuvvet alma i\u015fleminin tersidir. \\(b^y\\) \u00fcstel ifadesi \u201c\\(b\\) taban\u0131n\u0131 \\(y\\) kuvvetine y\u00fckseltince ne elde ederim?\u201d sorusunu sorarken, \\(\\log_b(x)\\) logaritmas\u0131 bunun tersini sorar: \u201c\\(x\\) say\u0131s\u0131n\u0131 elde etmek i\u00e7in \\(b\\) taban\u0131n\u0131 ka\u00e7\u0131nc\u0131 kuvvete y\u00fckseltmeliyim?\u201d \u00d6rne\u011fin \\(10^3 = 1000\\) oldu\u011fundan \\(\\log_{10}(1000) = 3\\)t\u00fcr. \\(b^y = x\\) ve \\(y = \\log_b(x)\\) ifadeleri tamamen ayn\u0131 bilgiyi ta\u015f\u0131r.<\/p>\n<p>\u00dc\u00e7 taban o kadar s\u0131k kullan\u0131l\u0131r ki kendilerine \u00f6zg\u00fc adlar\u0131 ve g\u00f6sterimleri vard\u0131r. <strong>Ortak logaritma<\/strong> taban\u0131 10'dur ve \\(\\log_{10}\\) ya da yaln\u0131zca log bi\u00e7iminde yaz\u0131l\u0131r; kimyada (pH), akustikte (desibel) ve depremlerde kullan\u0131lan Richter \u00f6l\u00e7e\u011finde kar\u015f\u0131m\u0131za \u00e7\u0131kar. <strong>Do\u011fal logaritma<\/strong> taban\u0131 \\(e \\approx 2.71828\\) olan logaritmad\u0131r ve ln olarak yaz\u0131l\u0131r; matematik analizde ve s\u00fcrekli b\u00fcy\u00fcme problemlerinde h\u00e2kim konumdad\u0131r. <strong>\u0130kili logaritma<\/strong> taban\u0131 2'dir ve \\(\\log_2\\) bi\u00e7iminde yaz\u0131l\u0131r; bilgisayar bilimlerinde temel bir yer tutar: ikili arama ve birle\u015ftirmeli s\u0131ralama gibi algoritmalardaki yar\u0131ya indirme ad\u0131mlar\u0131n\u0131n say\u0131s\u0131n\u0131 \u00f6l\u00e7er ve bir say\u0131y\u0131 temsil etmek i\u00e7in gereken bit say\u0131s\u0131n\u0131 verir.<\/p>\n<p>Sonucun yorumu tabana ba\u011fl\u0131d\u0131r. Taban\u0131 10 olan ve de\u011feri 3 olan bir logaritma \u201c\u00fc\u00e7 tane on \u00e7arpan\u0131\u201d anlam\u0131na gelir: \\(10 \\times 10 \\times 10\\). Sonucun tam say\u0131 olmamas\u0131, say\u0131n\u0131n taban\u0131n iki tam kuvveti aras\u0131nda kald\u0131\u011f\u0131n\u0131 g\u00f6sterir \u2014 \u00f6rne\u011fin \\(\\log_2(1000) \\approx 9.9658\\) sonucu, 1000'in \\(2^{10} = 1024\\)'\u00fcn hemen alt\u0131nda oldu\u011funu s\u00f6yler; 1000'in 10 bite s\u0131\u011fmas\u0131n\u0131n nedeni de budur.<\/p>\n<p>\\(\\log_b(x) = \\ln(x)\/\\ln(b)\\) taban de\u011fi\u015ftirme form\u00fcl\u00fc, t\u00fcm tabanlar aras\u0131ndaki pratik k\u00f6pr\u00fcd\u00fcr: bir t\u00fcr logaritmay\u0131 hesaplayabiliyorsan\u0131z hepsini hesaplayabilirsiniz. Bu hesaplay\u0131c\u0131n\u0131n 5 veya 2,5 gibi al\u0131\u015f\u0131lmad\u0131k tabanlarla da \u00e7al\u0131\u015fmas\u0131n\u0131n nedeni budur. Kuvvet ve k\u00f6klerle \u00e7al\u0131\u015f\u0131yorsan\u0131z <a href=\"https:\/\/wpcalc.com\/tr\/matematik\/ninci-kok\/\">n'inci K\u00f6k hesaplay\u0131c\u0131m\u0131z<\/a> kuvvet alman\u0131n \u00f6b\u00fcr y\u00fcz\u00fcn\u00fc halleder; <a href=\"https:\/\/wpcalc.com\/tr\/matematik\/geometrik-ortalama\/\">Geometrik Ortalama hesaplay\u0131c\u0131s\u0131<\/a> ise logaritmalar\u0131n \u00e7arp\u0131msal verilerdeki klasik bir uygulamas\u0131n\u0131 g\u00f6sterir.<\/p>\n<h2>Kurallar, Varsay\u0131mlar ve \u0130pu\u00e7lar\u0131<\/h2>\n<p><strong>Tan\u0131m k\u00fcmesi k\u0131s\u0131tlar\u0131.<\/strong> Logaritma yaln\u0131zca pozitif say\u0131lar ve ge\u00e7erli tabanlar i\u00e7in tan\u0131ml\u0131d\u0131r: \\(x &gt; 0\\), \\(b &gt; 0\\) ve \\(b \\neq 1\\). S\u0131f\u0131r\u0131n ve negatif say\u0131n\u0131n logaritmas\u0131 yoktur; 1 taban\u0131 ise elveri\u015fsizdir, \u00e7\u00fcnk\u00fc 1'in herhangi bir kuvveti daima 1 eder ve ba\u015fka hi\u00e7bir say\u0131y\u0131 \u00fcretemez. Hesaplay\u0131c\u0131 bu \u00fc\u00e7 ko\u015fulu da kontrol eder ve biri sa\u011flanmazsa hatan\u0131n nedenini a\u00e7\u0131klar.<\/p>\n<p>Logaritmalarla \u00e7al\u0131\u015f\u0131rken ak\u0131lda tutmaya de\u011fer <strong>faydal\u0131 \u00f6zellikler<\/strong>:<\/p>\n<ul>\n<li>\\(\\log_b(xy) = \\log_b(x) + \\log_b(y)\\) \u2014 \u00e7arp\u0131m\u0131n logaritmas\u0131, logaritmalar\u0131n toplam\u0131d\u0131r<\/li>\n<li>\\(\\log_b(x\/y) = \\log_b(x) - \\log_b(y)\\) \u2014 b\u00f6l\u00fcm\u00fcn logaritmas\u0131, logaritmalar\u0131n fark\u0131d\u0131r<\/li>\n<li>\\(\\log_b(x^n) = n \\log_b(x)\\) \u2014 kuvvetler \u00e7arpan olarak \u00f6ne \u00e7\u0131kar<\/li>\n<li>\\(\\log_b(b) = 1\\) ve her ge\u00e7erli taban i\u00e7in \\(\\log_b(1) = 0\\)<\/li>\n<\/ul>\n<p><strong>Yuvarlama.<\/strong> Sonu\u00e7lar 6 basamakl\u0131 ondal\u0131k g\u00f6sterimle yuvarlanarak g\u00f6r\u00fcnt\u00fclenir; bu y\u00fczden \\(b^{\\log_b(x)}\\) kontrol\u00fc, yuvarlama nedeniyle \\(x\\) de\u011ferinden son basamakta farkl\u0131 \u00e7\u0131kabilir \u2014 bu bir hata de\u011fil, beklenen bir durumdur.<\/p>\n<p><strong>Tam cevaplar.<\/strong> Ders kitaplar\u0131ndaki bir\u00e7ok problemin cevab\u0131 tam say\u0131d\u0131r: \\(\\log_2(8) = 3\\), \\(\\log_{10}(100) = 2\\), \\(\\log_5(125) = 3\\). Sonucunuz bir tam say\u0131ya \u00e7ok yak\u0131n \u00e7\u0131karsa (\u00f6rne\u011fin 2.999999), tam cevap neredeyse kesin olarak o tam say\u0131d\u0131r.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Herhangi bir pozitif say\u0131n\u0131n logaritmas\u0131n\u0131 istedi\u011finiz tabanda hesaplay\u0131n \u2014 2, 10, e (do\u011fal logaritma) veya \u00f6zel bir taban. Say\u0131y\u0131 girin, taban\u0131 se\u00e7in; sonu\u00e7la birlikte do\u011frulama ve kar\u015f\u0131la\u015ft\u0131rma i\u00e7in ortak, do\u011fal ve ikili logaritma de\u011ferlerini g\u00f6r\u00fcn.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[8],"tags":[16],"class_list":["post-4005","post","type-post","status-publish","format-standard","hentry","category-matematik","tag-cebir"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/4005","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/comments?post=4005"}],"version-history":[{"count":0,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/4005\/revisions"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/media?parent=4005"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/categories?post=4005"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/tags?post=4005"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}