To solve log\u20618(0.0625)\\log_8(0.0625)log8\u200b(0.0625), we can break the problem into smaller steps by expressing 0.0625 as a power of 8.<\/p>\n\n\n\n
Step 1: Express 0.0625 as a fraction<\/h3>\n\n\n\n
First, express 0.0625 as a fraction: 0.0625=1160.0625 = \\frac{1}{16}0.0625=161\u200b<\/p>\n\n\n\n
Step 2: Express 16 as a power of 8<\/h3>\n\n\n\n
We know that: 16=84316 = 8^{\\frac{4}{3}}16=834\u200b<\/p>\n\n\n\n
because 843=2123=24=168^{\\frac{4}{3}} = 2^{\\frac{12}{3}} = 2^4 = 16834\u200b=2312\u200b=24=16.<\/p>\n\n\n\n
Thus, we can write: 0.0625=18430.0625 = \\frac{1}{8^{\\frac{4}{3}}}0.0625=834\u200b1\u200b<\/p>\n\n\n\n
Step 3: Apply the logarithm rule<\/h3>\n\n\n\n
Now, let’s apply the logarithm rule: log\u20618(1843)=\u2212log\u20618(843)\\log_8\\left(\\frac{1}{8^{\\frac{4}{3}}}\\right) = -\\log_8\\left(8^{\\frac{4}{3}}\\right)log8\u200b(834\u200b1\u200b)=\u2212log8\u200b(834\u200b)<\/p>\n\n\n\n
Using the logarithmic property log\u2061b(bx)=x\\log_b(b^x) = xlogb\u200b(bx)=x, this becomes: \u221243-\\frac{4}{3}\u221234\u200b<\/p>\n\n\n\n
Final Answer:<\/h3>\n\n\n\n
Thus, log\u20618(0.0625)=\u221243\\log_8(0.0625) = -\\frac{4}{3}log8\u200b(0.0625)=\u221234\u200b.<\/p>\n\n\n\n
Explanation:<\/h3>\n\n\n\n
Logarithms are the inverse operations of exponents. In this case, log\u20618(0.0625)\\log_8(0.0625)log8\u200b(0.0625) is asking: “To what power must we raise 8 to get 0.0625?” By expressing 0.0625 as a fraction and relating it to powers of 8, we find that the answer is \u221243-\\frac{4}{3}\u221234\u200b, meaning that raising 8 to the power of \u221243-\\frac{4}{3}\u221234\u200b gives 0.0625.<\/p>\n\n\n\n Log base 8 0.0625 The Correct Answer and Explanation is: To solve log\u20618(0.0625)\\log_8(0.0625)log8\u200b(0.0625), we can break the problem into smaller steps by expressing 0.0625 as a power of 8. Step 1: Express 0.0625 as a fraction First, express 0.0625 as a fraction: 0.0625=1160.0625 = \\frac{1}{16}0.0625=161\u200b Step 2: Express 16 as a power of 8 We […]<\/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-250520","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/250520","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=250520"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/250520\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=250520"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=250520"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=250520"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-119.jpeg\")
<\/figure>\n","protected":false},"excerpt":{"rendered":"