{"id":183325,"date":"2025-01-16T07:56:27","date_gmt":"2025-01-16T07:56:27","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=183325"},"modified":"2025-01-16T07:56:29","modified_gmt":"2025-01-16T07:56:29","slug":"infinite-algebra-2-the-meaning-of-logarithms","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/01\/16\/infinite-algebra-2-the-meaning-of-logarithms\/","title":{"rendered":"Infinite Algebra 2 The Meaning Of Logarithms"},"content":{"rendered":"\n

Name Date Kuta Software – Infinite Algebra 2 The Meaning Of Logarithms Rewrite each equation in exponential form. 1) log, 36 = 2 2) log 289 17= 4) log, 81 = 4 3) log 14 196 – -2 Rewrite each equation in logarithmic form. 5) 60-8 6) 122 = 144 Rewrite each equation in exponential form. 10) log u= 4 Rewrite each equation in exponential form. 15 9) log 10) log, u=4 20 11) log, r = y 12) log 2 v = u 13) log, v=-16 14) log, x=-8 Rewrite each equation in logarithmic form. 15) -14 =v 16) 8′ = a 18) 6′ = x 1(3) – 1 Page \/ 2 – a + 19) 9′ = x 20) 69 = 123 Evaluate each expression. 21) log 64 22) logo 216 23) log, 16 24) log: 243 23) log, 16 24) log 3 243 25) log, 125 26) log, 4 27) log 343 7 28) log, 16 29) log 4 30) logo 216 Page 2\/2 – Q + Simplify cash expression. acer Simplify each expression. 31) 12l0512 144 32) slog, 17 33) xlog, 72 34) 9lo, 20 12 – Q +<\/p>\n\n\n\n

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

Here is the solution for each problem, followed by a 300-word explanation of the process:<\/p>\n\n\n\n

\n\n\n\n

Rewrite each equation in exponential form:<\/strong><\/h3>\n\n\n\n

1) ( \\log 6 36 = 2 ): ( 6^2 = 36 )
2) ( \\log 17 289 = 2 ): ( 17^2 = 289 )
3) ( \\log 14 196 = 2 ): ( 14^2 = 196 )
4) ( \\log 3 81 = 4 ): ( 3^4 = 81 )<\/p>\n\n\n\n

\n\n\n\n

Rewrite each equation in logarithmic form:<\/strong><\/h3>\n\n\n\n

5) ( 6^0 = 1 ): ( \\log 6 1 = 0 )
6) ( 12^2 = 144 ): ( \\log 12 144 = 2 )<\/p>\n\n\n\n

\n\n\n\n

Rewrite each equation in exponential form:<\/strong><\/h3>\n\n\n\n

10) ( \\log u = 4 ): ( 10^4 = u )
11) ( \\log 20 r = y ): ( 20^y = r )
12) ( \\log 2 v = u ): ( 2^u = v )
13) ( \\log 3 v = -16 ): ( 3^{-16} = v )
14) ( \\log 5 x = -8 ): ( 5^{-8} = x )<\/p>\n\n\n\n

\n\n\n\n

Rewrite each equation in logarithmic form:<\/strong><\/h3>\n\n\n\n

15) ( -14 = v ): ( \\log v (-14) = 1 )
16) ( 8^a = x ): ( \\log 8 x = a )
18) ( 6^x = 3 ): ( \\log 6 3 = x )<\/p>\n\n\n\n

\n\n\n\n

Evaluate each expression:<\/strong><\/h3>\n\n\n\n

21) ( \\log 2 64 ): ( 2^6 = 64 ), so ( \\log 2 64 = 6 )
22) ( \\log 6 216 ): ( 6^3 = 216 ), so ( \\log 6 216 = 3 )
23) ( \\log 2 16 ): ( 2^4 = 16 ), so ( \\log 2 16 = 4 )
24) ( \\log 3 243 ): ( 3^5 = 243 ), so ( \\log 3 243 = 5 )
25) ( \\log 5 125 ): ( 5^3 = 125 ), so ( \\log 5 125 = 3 )
26) ( \\log 2 4 ): ( 2^2 = 4 ), so ( \\log 2 4 = 2 )
27) ( \\log 7 343 ): ( 7^3 = 343 ), so ( \\log 7 343 = 3 )
28) ( \\log 4 16 ): ( 4^2 = 16 ), so ( \\log 4 16 = 2 )
29) ( \\log 6 36 ): ( 6^2 = 36 ), so ( \\log 6 36 = 2 )
30) ( \\log 6 216 ): ( 6^3 = 216 ), so ( \\log 6 216 = 3 )<\/p>\n\n\n\n

\n\n\n\n

Simplify expressions:<\/strong><\/h3>\n\n\n\n

31) ( \\log 12 (12^2) ): Simplifies to ( 2 )
32) ( 5 \\cdot \\log 7 7 ): Simplifies to ( 5 \\cdot 1 = 5 )
33) ( x \\cdot \\log 7 72 ): No simplification without more context.
34) ( 9 \\cdot \\log 5 20 ): No simplification without more context.<\/p>\n\n\n\n

\n\n\n\n

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

Logarithms are the inverse operation of exponents. If ( b^e = a ), then ( \\log b a = e ). This means the base ( b ) raised to the power ( e ) gives ( a ). Converting between logarithmic and exponential forms involves identifying the base, exponent, and result. For evaluation, find ( e ) that satisfies ( b^e = a ). Simplifications rely on logarithmic properties, such as ( \\log b (b^k) = k ).<\/p>\n","protected":false},"excerpt":{"rendered":"

Name Date Kuta Software – Infinite Algebra 2 The Meaning Of Logarithms Rewrite each equation in exponential form. 1) log, 36 = 2 2) log 289 17= 4) log, 81 = 4 3) log 14 196 – -2 Rewrite each equation in logarithmic form. 5) 60-8 6) 122 = 144 Rewrite each equation in exponential […]<\/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-183325","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/183325","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=183325"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/183325\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=183325"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=183325"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=183325"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}