{"id":232047,"date":"2025-06-11T16:25:16","date_gmt":"2025-06-11T16:25:16","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=232047"},"modified":"2025-06-11T16:25:18","modified_gmt":"2025-06-11T16:25:18","slug":"what-is-the-value-of-log2-128","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/11\/what-is-the-value-of-log2-128\/","title":{"rendered":"What is the value of log2 128"},"content":{"rendered":"\n<p>What is the value of log2 128?<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<h6 class=\"wp-block-heading\">ChatGPT said:<\/h6>\n\n\n\n<p><strong>Answer:<\/strong>log\u20612128=7\\log_2 128 = 7log2\u200b128=7<\/p>\n\n\n\n<p><strong>Explanation:<\/strong><br>To understand the value of log\u20612128\\log_2 128log2\u200b128, begin by recalling what a logarithm represents. The logarithmic expression log\u2061ba=x\\log_b a = xlogb\u200ba=x means that bx=ab^x = abx=a. In this case, the base b=2b = 2b=2, and the number a=128a = 128a=128. The question asks: \u201cTo what power must 2 be raised to get 128?\u201d<\/p>\n\n\n\n<p>This can be solved by expressing 128 as a power of 2.<\/p>\n\n\n\n<p>Start with repeated multiplication:21=222=423=824=1625=3226=6427=128\\begin{align*} 2^1 &amp;= 2 \\\\ 2^2 &amp;= 4 \\\\ 2^3 &amp;= 8 \\\\ 2^4 &amp;= 16 \\\\ 2^5 &amp;= 32 \\\\ 2^6 &amp;= 64 \\\\ 2^7 &amp;= 128 \\end{align*}21222324252627\u200b=2=4=8=16=32=64=128\u200b<\/p>\n\n\n\n<p>So, 27=1282^7 = 12827=128. That means 2 must be raised to the power of 7 to obtain 128. By the definition of logarithms:log\u20612128=7\\log_2 128 = 7log2\u200b128=7<\/p>\n\n\n\n<p>This result makes sense because the logarithm is the inverse operation of exponentiation. When evaluating a logarithmic expression, the goal is to find the exponent that makes the base equal to the given number.<\/p>\n\n\n\n<p>In general, if a number is a power of 2, then its base-2 logarithm is simply the exponent. Since 128=27128 = 2^7128=27, the base-2 logarithm of 128 is 7.<\/p>\n\n\n\n<p>Logarithms have many applications in mathematics, science, and computer science. Base-2 logarithms, in particular, are useful in analyzing algorithms, especially in computer science, because binary systems operate using powers of 2. For example, the time complexity of certain efficient algorithms is expressed using base-2 logarithms.<\/p>\n\n\n\n<p>Understanding logarithms helps with simplifying large computations, solving exponential equations, and analyzing growth or decay processes. The concept also plays a key role in fields such as signal processing, information theory, and cryptography.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-270.jpeg\" alt=\"\" class=\"wp-image-232048\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>What is the value of log2 128? The Correct Answer and Explanation is: ChatGPT said: Answer:log\u20612128=7\\log_2 128 = 7log2\u200b128=7 Explanation:To understand the value of log\u20612128\\log_2 128log2\u200b128, begin by recalling what a logarithm represents. The logarithmic expression log\u2061ba=x\\log_b a = xlogb\u200ba=x means that bx=ab^x = abx=a. In this case, the base b=2b = 2b=2, and the [&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-232047","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/232047","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=232047"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/232047\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=232047"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=232047"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=232047"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}