{"id":619,"date":"2025-01-27T17:00:31","date_gmt":"2025-01-27T11:15:31","guid":{"rendered":"https:\/\/pokharelsugam.com.np\/bioinformatics\/?p=619"},"modified":"2025-01-27T17:53:42","modified_gmt":"2025-01-27T12:08:42","slug":"logarithm","status":"publish","type":"post","link":"https:\/\/pokharelsugam.com.np\/bioinformatics\/logarithm\/","title":{"rendered":"Logarithm"},"content":{"rendered":"\n<script type=\"text\/javascript\" async \n  src=\"https:\/\/cdnjs.cloudflare.com\/ajax\/libs\/mathjax\/2.7.7\/MathJax.js?config=TeX-MML-AM_CHTML\">\n<\/script>\n\n\n\n<p class=\"has-medium-font-size\"><strong>Definition of Logarithm<\/strong>:<br>\\(\\text{If and only if } y = a^x ), where ( a > 0 ), ( a \\neq 1 ), and ( x > 0 \\)<br>\\(\\log_a y = x \\)<\/p>\n\n\n\n<p class=\"has-medium-font-size\"><strong>Types of Log<\/strong>:<br><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">1. Common log ( \\(\\log_{10} x \\) )<\/mark><br>Also written as  <mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-0-color\">\\(\\log x \\)<\/mark><br><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-8-color\">2. Natural log ( \\(\\log_{2.71828} x \\) )<\/mark><br>Also written as  <mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-0-color\">\\(\\log_e x \\)<\/mark> or <mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-0-color\">\\(\\ln x \\)<\/mark><\/p>\n\n\n\n<p class=\"has-medium-font-size\"><strong>Logarithm of 1<\/strong>:<br>\\( \\log_a 1 = 0  \\)<\/p>\n\n\n\n<p class=\"has-medium-font-size\"><strong>Logarithm of the Base<\/strong>:<br>\\( \\log_a a = 1 \\)<\/p>\n\n\n\n<p class=\"has-medium-font-size\">\\( \\log_a a^x = x \\)<br>\\( a^{\\log_a x} = x \\)<br>\\( e^{\\ln x} = x \\)<br>\\( a^{b\\log_a x} = x^b \\)<\/p>\n\n\n\n<p class=\"has-medium-font-size\"><strong>Logarithm of Reciprocal<\/strong>:<br>\\( \\log_a\\left(\\frac{1}{x}\\right) = -\\log_a x \\)<\/p>\n\n\n\n<p class=\"has-medium-font-size\"><strong>Product Rule<\/strong>:<br>\\( \\log_a(x.y) = \\log_a x + \\log_a y \\)<\/p>\n\n\n\n<p class=\"has-medium-font-size\"><strong>Quotient Rule<\/strong>:<br>\\( \\log_a\\left(\\frac{x}{y}\\right) = \\log_a x &#8211; \\log_a y \\)<\/p>\n\n\n\n<p class=\"has-medium-font-size\"><strong>Power Rule<\/strong>:<br>\\( \\log_a x^n = n \\cdot \\log_a x \\)<\/p>\n\n\n\n<p class=\"has-medium-font-size\"><strong>Compression Rule<\/strong>:<br>\\( \\log_a(x^m.y^n) = m \\cdot \\log_a x + n \\cdot \\log_a y \\)<\/p>\n\n\n\n<p class=\"has-medium-font-size\"><strong>Logarithmic Expansion<\/strong>: <br><strong>For \\( x = a \\cdot b \\cdot c \\)<\/strong><br>\\( \\log_a x = \\log_a a + \\log_a b + \\log_a c \\)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Definition of Logarithm:\\(\\text{If and only if } y = a^x ), where ( a > 0 ), ( a \\neq [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_uag_custom_page_level_css":"","site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[16,15],"tags":[],"class_list":["post-619","post","type-post","status-publish","format-standard","hentry","category-mathematics","category-mathematics-algorithm"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Logarithm - Bioinformatics Notes<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/pokharelsugam.com.np\/bioinformatics\/logarithm\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Logarithm - Bioinformatics Notes\" \/>\n<meta property=\"og:description\" content=\"Definition of Logarithm:(text{If and only if } y = a^x ), where ( a &gt; 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