{"id":225017,"date":"2025-06-03T18:35:17","date_gmt":"2025-06-03T18:35:17","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=225017"},"modified":"2025-06-03T18:35:19","modified_gmt":"2025-06-03T18:35:19","slug":"use-the-power-property-to-rewrite-loga%c6%929","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/03\/use-the-power-property-to-rewrite-loga%c6%929\/","title":{"rendered":"Use the power property to rewrite log\u00e2\u201a\u0192(9)."},"content":{"rendered":"\n

Use the power property to rewrite log\u00e2\u201a\u0192(9).<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Final Answer:<\/h3>\n\n\n\n

log\u20613(9)=log\u20613(32)=2\\log_3(9) = \\log_3(3^2) = 2<\/p>\n\n\n\n

\n\n\n\n

Explanation <\/h3>\n\n\n\n

To simplify log\u20613(9)\\log_3(9) using the power property of logarithms<\/strong>, we first need to express 9 as a power of the base 3.<\/p>\n\n\n\n

Step 1: Express the number as a power of the base<\/h4>\n\n\n\n

Notice that: 9=329 = 3^2<\/p>\n\n\n\n

So, we rewrite the logarithm: log\u20613(9)=log\u20613(32)\\log_3(9) = \\log_3(3^2)<\/p>\n\n\n\n

Step 2: Apply the power property of logarithms<\/h4>\n\n\n\n

The power property<\/strong> states that: log\u2061b(an)=n\u22c5log\u2061b(a)\\log_b(a^n) = n \\cdot \\log_b(a)<\/p>\n\n\n\n

Here, a=3a = 3, n=2n = 2, and b=3b = 3. Applying the rule: log\u20613(32)=2\u22c5log\u20613(3)\\log_3(3^2) = 2 \\cdot \\log_3(3)<\/p>\n\n\n\n

Step 3: Simplify using the identity log\u2061b(b)=1\\log_b(b) = 1<\/h4>\n\n\n\n

log\u20613(3)=1\\log_3(3) = 1<\/p>\n\n\n\n

So: 2\u22c5log\u20613(3)=2\u22c51=22 \\cdot \\log_3(3) = 2 \\cdot 1 = 2<\/p>\n\n\n\n

Thus, log\u20613(9)=2\\log_3(9) = 2<\/p>\n\n\n\n

\n\n\n\n

Why This Works:<\/h3>\n\n\n\n

Logarithms are the inverse of exponents. That means: log\u2061b(a)=cmeansbc=a\\log_b(a) = c \\quad \\text{means} \\quad b^c = a<\/p>\n\n\n\n

In this problem: log\u20613(9)=xmeans3x=9\\log_3(9) = x \\quad \\text{means} \\quad 3^x = 9<\/p>\n\n\n\n

Since 32=93^2 = 9, then x=2x = 2. So the logarithm equals 2.<\/p>\n\n\n\n

Using the power property<\/strong> helps us simplify logarithms by pulling exponents down as multipliers. This is especially useful when the argument inside the logarithm is a perfect power of the base.<\/p>\n\n\n\n

This rule is commonly used in algebra and calculus to simplify expressions, solve exponential equations, or differentiate logarithmic functions.<\/p>\n\n\n\n

\"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

Use the power property to rewrite log\u00e2\u201a\u0192(9). The Correct Answer and Explanation is: Final Answer: log\u20613(9)=log\u20613(32)=2\\log_3(9) = \\log_3(3^2) = 2 Explanation To simplify log\u20613(9)\\log_3(9) using the power property of logarithms, we first need to express 9 as a power of the base 3. Step 1: Express the number as a power of the base Notice […]<\/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-225017","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/225017","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=225017"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/225017\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=225017"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=225017"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=225017"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}