{"id":194988,"date":"2025-02-25T10:44:51","date_gmt":"2025-02-25T10:44:51","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=194988"},"modified":"2025-02-25T10:44:54","modified_gmt":"2025-02-25T10:44:54","slug":"evaluate-the-following-log_1024-2-log_1015-4-log_10125","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/25\/evaluate-the-following-log_1024-2-log_1015-4-log_10125\/","title":{"rendered":"Evaluate the following: log_10(24) + 2 * log_10(15) &#8211; 4 * log_10(125)"},"content":{"rendered":"\n<p>Evaluate the following: log_10(24) + 2 * log_10(15) &#8211; 4 * log_10(125)<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/02\/image-1500-1024x688.png\" alt=\"\" class=\"wp-image-194989\"\/><\/figure>\n\n\n\n<p>The evaluated result of the given logarithmic expression:<\/p>\n\n\n\n<p>[<br>\\log_{10}(24) + 2 \\cdot \\log_{10}(15) &#8211; 4 \\cdot \\log_{10}(125)<br>]<\/p>\n\n\n\n<p>is <strong>-4.655<\/strong> (approximately).<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>We simplify the expression step by step using logarithmic properties.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Step 1: Expanding Logarithmic Terms<\/h4>\n\n\n\n<p>Using the logarithmic identity:<\/p>\n\n\n\n<p>[<br>\\log(a^b) = b \\log(a)<br>]<\/p>\n\n\n\n<p>we rewrite:<\/p>\n\n\n\n<p>[<br>2 \\log_{10}(15) = \\log_{10}(15^2) = \\log_{10}(225)<br>]<\/p>\n\n\n\n<p>[<br>4 \\log_{10}(125) = \\log_{10}(125^4) = \\log_{10}(244140625)<br>]<\/p>\n\n\n\n<p>Thus, the given expression transforms into:<\/p>\n\n\n\n<p>[<br>\\log_{10}(24) + \\log_{10}(225) &#8211; \\log_{10}(244140625)<br>]<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Step 2: Applying Logarithmic Properties<\/h4>\n\n\n\n<p>Using the identity:<\/p>\n\n\n\n<p>[<br>\\log(a) + \\log(b) = \\log(a \\cdot b)<br>]<\/p>\n\n\n\n<p>we combine:<\/p>\n\n\n\n<p>[<br>\\log_{10}(24 \\times 225) = \\log_{10}(5400)<br>]<\/p>\n\n\n\n<p>Then applying:<\/p>\n\n\n\n<p>[<br>\\log(a) &#8211; \\log(b) = \\log\\left(\\frac{a}{b}\\right)<br>]<\/p>\n\n\n\n<p>we simplify:<\/p>\n\n\n\n<p>[<br>\\log_{10} \\left(\\frac{5400}{244140625}\\right)<br>]<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Step 3: Calculating the Logarithm<\/h4>\n\n\n\n<p>Computing:<\/p>\n\n\n\n<p>[<br>\\frac{5400}{244140625} \\approx 2.211 \\times 10^{-5}<br>]<\/p>\n\n\n\n<p>Taking the base-10 logarithm:<\/p>\n\n\n\n<p>[<br>\\log_{10}(2.211 \\times 10^{-5}) = \\log_{10}(2.211) + \\log_{10}(10^{-5})<br>]<\/p>\n\n\n\n<p>Approximating:<\/p>\n\n\n\n<p>[<br>\\log_{10}(2.211) \\approx 0.345<br>]<\/p>\n\n\n\n<p>[<br>\\log_{10}(10^{-5}) = -5<br>]<\/p>\n\n\n\n<p>So,<\/p>\n\n\n\n<p>[<br>0.345 &#8211; 5 = -4.655<br>]<\/p>\n\n\n\n<p>Thus, the final result is <strong>-4.655<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Summary:<\/h3>\n\n\n\n<p>The logarithmic expression simplifies to approximately <strong>-4.655<\/strong>, and the graph above represents the logarithmic function, highlighting key values.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Evaluate the following: log_10(24) + 2 * log_10(15) &#8211; 4 * log_10(125) The Correct Answer and Explanation is : The evaluated result of the given logarithmic expression: [\\log_{10}(24) + 2 \\cdot \\log_{10}(15) &#8211; 4 \\cdot \\log_{10}(125)] is -4.655 (approximately). Explanation: We simplify the expression step by step using logarithmic properties. Step 1: Expanding Logarithmic Terms [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"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":"","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-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":"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":""},"mobile":{"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":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-194988","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/194988","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=194988"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/194988\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=194988"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=194988"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=194988"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}