{"id":238815,"date":"2025-06-18T11:50:22","date_gmt":"2025-06-18T11:50:22","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=238815"},"modified":"2025-06-18T11:50:24","modified_gmt":"2025-06-18T11:50:24","slug":"which-is-equal-to-log2-0-5","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/18\/which-is-equal-to-log2-0-5\/","title":{"rendered":"Which is equal to log2 0.5"},"content":{"rendered":"\n<p>Which is equal to log2 0.5? Select the correct answer below: 0.5 -0.5 2 -2 -1<\/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<p>The correct answer is: <strong>-1<\/strong><\/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 are asked to evaluate:<br><strong>log\u2082(0.5)<\/strong><\/p>\n\n\n\n<p>This means:<br>&#8220;To what power must 2 be raised to get 0.5?&#8221;<\/p>\n\n\n\n<p>In other words:<br><strong>2^x = 0.5<\/strong><\/p>\n\n\n\n<p>Now think about the relationship between 2 and 0.5.<\/p>\n\n\n\n<p>We know that:<br><strong>2^(-1) = 1 \/ 2 = 0.5<\/strong><\/p>\n\n\n\n<p>Therefore:<br><strong>x = -1<\/strong><\/p>\n\n\n\n<p>So:<br><strong>log\u2082(0.5) = -1<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Why this is true:<\/h3>\n\n\n\n<p>The logarithm function is the inverse of the exponential function. So when we take a logarithm, we are asking the exponent that gives us a certain number.<\/p>\n\n\n\n<p>In general, for any base bbb and positive number aaa:log\u2061b(a)=xif&nbsp;and&nbsp;only&nbsp;ifbx=a\\log_b(a) = x \\quad \\text{if and only if} \\quad b^x = alogb\u200b(a)=xif&nbsp;and&nbsp;only&nbsp;ifbx=a<\/p>\n\n\n\n<p>Here, our base is 2 and our number is 0.5. Since 0.5 is less than 1, the logarithm will be <strong>negative<\/strong>. That\u2019s because any base raised to a negative exponent gives a fraction between 0 and 1.<\/p>\n\n\n\n<p>Let\u2019s verify the other choices quickly:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>0.5<\/strong>: 20.5\u22481.412^{0.5} \\approx 1.4120.5\u22481.41, which is greater than 0.5, so not correct<\/li>\n\n\n\n<li><strong>-0.5<\/strong>: 2\u22120.5\u22480.7072^{-0.5} \\approx 0.7072\u22120.5\u22480.707, not equal to 0.5<\/li>\n\n\n\n<li><strong>2<\/strong>: 22=42^2 = 422=4, incorrect<\/li>\n\n\n\n<li><strong>-2<\/strong>: 2\u22122=1\/4=0.252^{-2} = 1\/4 = 0.252\u22122=1\/4=0.25, too small<\/li>\n\n\n\n<li><strong>-1<\/strong>: 2\u22121=1\/2=0.52^{-1} = 1\/2 = 0.52\u22121=1\/2=0.5, correct<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<p><strong>log\u2082(0.5) = -1<\/strong> \u2705<\/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-banner8-1089.jpeg\" alt=\"\" class=\"wp-image-238816\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Which is equal to log2 0.5? Select the correct answer below: 0.5 -0.5 2 -2 -1 The Correct Answer and Explanation is: The correct answer is: -1 Explanation: We are asked to evaluate:log\u2082(0.5) This means:&#8220;To what power must 2 be raised to get 0.5?&#8221; In other words:2^x = 0.5 Now think about the relationship between [&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-238815","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/238815","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=238815"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/238815\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=238815"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=238815"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=238815"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}