Expressing Logarithms in Exponential Form<\/h3>\n\n\n\n\n- log\u2081(256) = 2<\/strong> Exponential Form:<\/strong> 12=2561^2 = 25612=256 Explanation:<\/strong>
The logarithmic form log\u2061a(b)=c\\log_a(b) = cloga\u200b(b)=c translates to the exponential form ac=ba^c = bac=b. Here, the base is 1, the exponent is 2, and the result is 256. However, this equation is invalid in real numbers because any power of 1 is always 1. So, there\u2019s no real solution to this equation.<\/li>\n\n\n\n- log\u2080\u2084(2) = 2<\/strong> Exponential Form:<\/strong> 42=24^2 = 242=2 Explanation:<\/strong>
Again, applying the logarithmic-to-exponential conversion, the base is 4, the exponent is 2, and the result is 2. But 42=164^2 = 1642=16, not 2, so this equation is incorrect or invalid.<\/li>\n\n\n\n- log\u2081\u2088(289)<\/strong> Exponential Form:<\/strong> 18x=28918^x = 28918x=289 Explanation:<\/strong>
Here, the base is 18, and log\u206118(289)\\log\u2081\u2088(289)log18\u200b(289) is equivalent to solving 18x=28918^x = 28918x=289. You can find xxx by taking the logarithm of both sides, but the exact answer would require a calculator to solve numerically.<\/li>\n<\/ol>\n\n\n\n
\n\n\n\nExpressing Exponentials in Logarithmic Form<\/h3>\n\n\n\n\n- 243 = 3\u2076<\/strong> Logarithmic Form:<\/strong> log\u20613(243)=6\\log\u2083(243) = 6log3\u200b(243)=6 Explanation:<\/strong>
The exponential form ab=ca^b = cab=c is equivalent to the logarithmic form log\u2061a(c)=b\\log_a(c) = bloga\u200b(c)=b. Here, 36=2433^6 = 24336=243, so log\u20613(243)=6\\log\u2083(243) = 6log3\u200b(243)=6.<\/li>\n\n\n\n- 7\u2075 = 196<\/strong> Logarithmic Form:<\/strong> log\u20617(196)=5\\log\u2087(196) = 5log7\u200b(196)=5 Explanation:<\/strong>
The exponential equation 75=1967^5 = 19675=196 becomes log\u20617(196)=5\\log\u2087(196) = 5log7\u200b(196)=5, where the base is 7, the result is 196, and the exponent is 5.<\/li>\n\n\n\n- 156<\/strong> Logarithmic Form:<\/strong> log\u2061156(x)=y\\log_{156}(x) = ylog156\u200b(x)=y Explanation:<\/strong>
This is simply a placeholder, and we\u2019d need the context of an equation to rewrite it properly. If you had something like 156y=x156^y = x156y=x, then it would be written as log\u2061156(x)=y\\log_{156}(x) = ylog156\u200b(x)=y.<\/li>\n<\/ol>\n\n\n\n
\n\n\n\nEvaluating Logarithms<\/h3>\n\n\n\n\n- log\u2089(64)<\/strong> Exponential Form:<\/strong> 9x=649^x = 649x=64 Explanation:<\/strong>
Rewriting the logarithm as an exponential, we find 9x=649^x = 649x=64. To solve for xxx, take the logarithm of both sides: x=log\u2061(64)log\u2061(9)x = \\frac{\\log(64)}{\\log(9)}x=log(9)log(64)\u200b Numerically, this will give you the answer.<\/li>\n\n\n\n- log\u2081\u2080(10,000)<\/strong> Exponential Form:<\/strong> 10x=10,00010^x = 10,00010x=10,000 Explanation:<\/strong>
Since 10,000=10410,000 = 10^410,000=104, log\u206110(10,000)=4\\log_{10}(10,000) = 4log10\u200b(10,000)=4.<\/li>\n\n\n\n- log\u2088(2\u00b3)<\/strong> Exponential Form:<\/strong> 8x=238^x = 2^38x=23 Explanation:<\/strong>
Since 8=238 = 2^38=23, this becomes: 23x=232^{3x} = 2^323x=23 Solving for xxx, we find x=1x = 1x=1.<\/li>\n\n\n\n- log\u2083(27)<\/strong> Exponential Form:<\/strong> 3x=273^x = 273x=27 Explanation:<\/strong>
Since 27=3327 = 3^327=33, log\u20613(27)=3\\log\u2083(27) = 3log3\u200b(27)=3.<\/li>\n<\/ol>\n\n\n\n
\n\n\n\nWriting Inverses of Exponentials and Logarithms<\/h3>\n\n\n\n\n- log\u2080(x + 1)<\/strong> Inverse:<\/strong> y=x+1y = x + 1y=x+1 Explanation:<\/strong>
To find the inverse, swap xxx and yyy and solve for yyy. The result is y=x+1y = x + 1y=x+1, which is a linear function, the inverse of the logarithm.<\/li>\n\n\n\n- y = 2\u02e3<\/strong> Inverse:<\/strong> log\u20612(y)=x\\log\u2082(y) = xlog2\u200b(y)=x Explanation:<\/strong>
The inverse of an exponential function y=axy = a^xy=ax is a logarithmic function. So, to find the inverse of y=2xy = 2^xy=2x, write it as log\u20612(y)=x\\log\u2082(y) = xlog2\u200b(y)=x.<\/li>\n<\/ol>\n\n\n\n
\n\n\n\nThese examples should give you a solid understanding of the relationships between logarithmic and exponential forms.<\/p>\n\n\n\n![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner5-738.jpeg\")
<\/figure>\n","protected":false},"excerpt":{"rendered":"Expressing Logarithms in Exponential Form: Rewrite each logarithmic equation in exponential form. Hint: Remember the acronyms “logs are BAE” and “exponentials are B-E-A-utiful.” 1. log\u00e2\u201a\u0081(256) = 2 2. log\u00e2\u201a\u20ac\u00e2\u201a\u201e(2) = 2 3. log\u00e2\u201a\u0081\u00e2\u201a\u2021(289) 4. log\u00e1\u00b5\u00a3 Expressing Exponentials in Logarithmic Form: Rewrite each exponential equation in logarithmic form. 1. 243 = log\u00e2\u201a\u0192\u00e2\u201a\u201a\u00e2\u201a\u201e(18) 2. 7\u00e2\u0081\u00b4 = 196 […]<\/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-245880","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/245880","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=245880"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/245880\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=245880"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=245880"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=245880"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
The logarithmic form log\u2061a(b)=c\\log_a(b) = cloga\u200b(b)=c translates to the exponential form ac=ba^c = bac=b. Here, the base is 1, the exponent is 2, and the result is 256. However, this equation is invalid in real numbers because any power of 1 is always 1. So, there\u2019s no real solution to this equation.<\/li>\n\n\n\n
Again, applying the logarithmic-to-exponential conversion, the base is 4, the exponent is 2, and the result is 2. But 42=164^2 = 1642=16, not 2, so this equation is incorrect or invalid.<\/li>\n\n\n\n
Here, the base is 18, and log\u206118(289)\\log\u2081\u2088(289)log18\u200b(289) is equivalent to solving 18x=28918^x = 28918x=289. You can find xxx by taking the logarithm of both sides, but the exact answer would require a calculator to solve numerically.<\/li>\n<\/ol>\n\n\n\n
\n\n\n\n
Expressing Exponentials in Logarithmic Form<\/h3>\n\n\n\n\n- 243 = 3\u2076<\/strong> Logarithmic Form:<\/strong> log\u20613(243)=6\\log\u2083(243) = 6log3\u200b(243)=6 Explanation:<\/strong>
The exponential form ab=ca^b = cab=c is equivalent to the logarithmic form log\u2061a(c)=b\\log_a(c) = bloga\u200b(c)=b. Here, 36=2433^6 = 24336=243, so log\u20613(243)=6\\log\u2083(243) = 6log3\u200b(243)=6.<\/li>\n\n\n\n- 7\u2075 = 196<\/strong> Logarithmic Form:<\/strong> log\u20617(196)=5\\log\u2087(196) = 5log7\u200b(196)=5 Explanation:<\/strong>
The exponential equation 75=1967^5 = 19675=196 becomes log\u20617(196)=5\\log\u2087(196) = 5log7\u200b(196)=5, where the base is 7, the result is 196, and the exponent is 5.<\/li>\n\n\n\n- 156<\/strong> Logarithmic Form:<\/strong> log\u2061156(x)=y\\log_{156}(x) = ylog156\u200b(x)=y Explanation:<\/strong>
This is simply a placeholder, and we\u2019d need the context of an equation to rewrite it properly. If you had something like 156y=x156^y = x156y=x, then it would be written as log\u2061156(x)=y\\log_{156}(x) = ylog156\u200b(x)=y.<\/li>\n<\/ol>\n\n\n\n
\n\n\n\nEvaluating Logarithms<\/h3>\n\n\n\n\n- log\u2089(64)<\/strong> Exponential Form:<\/strong> 9x=649^x = 649x=64 Explanation:<\/strong>
Rewriting the logarithm as an exponential, we find 9x=649^x = 649x=64. To solve for xxx, take the logarithm of both sides: x=log\u2061(64)log\u2061(9)x = \\frac{\\log(64)}{\\log(9)}x=log(9)log(64)\u200b Numerically, this will give you the answer.<\/li>\n\n\n\n- log\u2081\u2080(10,000)<\/strong> Exponential Form:<\/strong> 10x=10,00010^x = 10,00010x=10,000 Explanation:<\/strong>
Since 10,000=10410,000 = 10^410,000=104, log\u206110(10,000)=4\\log_{10}(10,000) = 4log10\u200b(10,000)=4.<\/li>\n\n\n\n- log\u2088(2\u00b3)<\/strong> Exponential Form:<\/strong> 8x=238^x = 2^38x=23 Explanation:<\/strong>
Since 8=238 = 2^38=23, this becomes: 23x=232^{3x} = 2^323x=23 Solving for xxx, we find x=1x = 1x=1.<\/li>\n\n\n\n- log\u2083(27)<\/strong> Exponential Form:<\/strong> 3x=273^x = 273x=27 Explanation:<\/strong>
Since 27=3327 = 3^327=33, log\u20613(27)=3\\log\u2083(27) = 3log3\u200b(27)=3.<\/li>\n<\/ol>\n\n\n\n
\n\n\n\nWriting Inverses of Exponentials and Logarithms<\/h3>\n\n\n\n\n- log\u2080(x + 1)<\/strong> Inverse:<\/strong> y=x+1y = x + 1y=x+1 Explanation:<\/strong>
To find the inverse, swap xxx and yyy and solve for yyy. The result is y=x+1y = x + 1y=x+1, which is a linear function, the inverse of the logarithm.<\/li>\n\n\n\n- y = 2\u02e3<\/strong> Inverse:<\/strong> log\u20612(y)=x\\log\u2082(y) = xlog2\u200b(y)=x Explanation:<\/strong>
The inverse of an exponential function y=axy = a^xy=ax is a logarithmic function. So, to find the inverse of y=2xy = 2^xy=2x, write it as log\u20612(y)=x\\log\u2082(y) = xlog2\u200b(y)=x.<\/li>\n<\/ol>\n\n\n\n
\n\n\n\nThese examples should give you a solid understanding of the relationships between logarithmic and exponential forms.<\/p>\n\n\n\n<\/figure>\n","protected":false},"excerpt":{"rendered":"Expressing Logarithms in Exponential Form: Rewrite each logarithmic equation in exponential form. Hint: Remember the acronyms “logs are BAE” and “exponentials are B-E-A-utiful.” 1. log\u00e2\u201a\u0081(256) = 2 2. log\u00e2\u201a\u20ac\u00e2\u201a\u201e(2) = 2 3. log\u00e2\u201a\u0081\u00e2\u201a\u2021(289) 4. log\u00e1\u00b5\u00a3 Expressing Exponentials in Logarithmic Form: Rewrite each exponential equation in logarithmic form. 1. 243 = log\u00e2\u201a\u0192\u00e2\u201a\u201a\u00e2\u201a\u201e(18) 2. 7\u00e2\u0081\u00b4 = 196 […]<\/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-245880","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/245880","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=245880"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/245880\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=245880"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=245880"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=245880"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
The exponential form ab=ca^b = cab=c is equivalent to the logarithmic form log\u2061a(c)=b\\log_a(c) = bloga\u200b(c)=b. Here, 36=2433^6 = 24336=243, so log\u20613(243)=6\\log\u2083(243) = 6log3\u200b(243)=6.<\/li>\n\n\n\n
The exponential equation 75=1967^5 = 19675=196 becomes log\u20617(196)=5\\log\u2087(196) = 5log7\u200b(196)=5, where the base is 7, the result is 196, and the exponent is 5.<\/li>\n\n\n\n
This is simply a placeholder, and we\u2019d need the context of an equation to rewrite it properly. If you had something like 156y=x156^y = x156y=x, then it would be written as log\u2061156(x)=y\\log_{156}(x) = ylog156\u200b(x)=y.<\/li>\n<\/ol>\n\n\n\n
\n\n\n\n
Evaluating Logarithms<\/h3>\n\n\n\n\n- log\u2089(64)<\/strong> Exponential Form:<\/strong> 9x=649^x = 649x=64 Explanation:<\/strong>
Rewriting the logarithm as an exponential, we find 9x=649^x = 649x=64. To solve for xxx, take the logarithm of both sides: x=log\u2061(64)log\u2061(9)x = \\frac{\\log(64)}{\\log(9)}x=log(9)log(64)\u200b Numerically, this will give you the answer.<\/li>\n\n\n\n- log\u2081\u2080(10,000)<\/strong> Exponential Form:<\/strong> 10x=10,00010^x = 10,00010x=10,000 Explanation:<\/strong>
Since 10,000=10410,000 = 10^410,000=104, log\u206110(10,000)=4\\log_{10}(10,000) = 4log10\u200b(10,000)=4.<\/li>\n\n\n\n- log\u2088(2\u00b3)<\/strong> Exponential Form:<\/strong> 8x=238^x = 2^38x=23 Explanation:<\/strong>
Since 8=238 = 2^38=23, this becomes: 23x=232^{3x} = 2^323x=23 Solving for xxx, we find x=1x = 1x=1.<\/li>\n\n\n\n- log\u2083(27)<\/strong> Exponential Form:<\/strong> 3x=273^x = 273x=27 Explanation:<\/strong>
Since 27=3327 = 3^327=33, log\u20613(27)=3\\log\u2083(27) = 3log3\u200b(27)=3.<\/li>\n<\/ol>\n\n\n\n
\n\n\n\nWriting Inverses of Exponentials and Logarithms<\/h3>\n\n\n\n\n- log\u2080(x + 1)<\/strong> Inverse:<\/strong> y=x+1y = x + 1y=x+1 Explanation:<\/strong>
To find the inverse, swap xxx and yyy and solve for yyy. The result is y=x+1y = x + 1y=x+1, which is a linear function, the inverse of the logarithm.<\/li>\n\n\n\n- y = 2\u02e3<\/strong> Inverse:<\/strong> log\u20612(y)=x\\log\u2082(y) = xlog2\u200b(y)=x Explanation:<\/strong>
The inverse of an exponential function y=axy = a^xy=ax is a logarithmic function. So, to find the inverse of y=2xy = 2^xy=2x, write it as log\u20612(y)=x\\log\u2082(y) = xlog2\u200b(y)=x.<\/li>\n<\/ol>\n\n\n\n
\n\n\n\nThese examples should give you a solid understanding of the relationships between logarithmic and exponential forms.<\/p>\n\n\n\n<\/figure>\n","protected":false},"excerpt":{"rendered":"Expressing Logarithms in Exponential Form: Rewrite each logarithmic equation in exponential form. Hint: Remember the acronyms “logs are BAE” and “exponentials are B-E-A-utiful.” 1. log\u00e2\u201a\u0081(256) = 2 2. log\u00e2\u201a\u20ac\u00e2\u201a\u201e(2) = 2 3. log\u00e2\u201a\u0081\u00e2\u201a\u2021(289) 4. log\u00e1\u00b5\u00a3 Expressing Exponentials in Logarithmic Form: Rewrite each exponential equation in logarithmic form. 1. 243 = log\u00e2\u201a\u0192\u00e2\u201a\u201a\u00e2\u201a\u201e(18) 2. 7\u00e2\u0081\u00b4 = 196 […]<\/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-245880","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/245880","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=245880"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/245880\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=245880"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=245880"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=245880"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
Rewriting the logarithm as an exponential, we find 9x=649^x = 649x=64. To solve for xxx, take the logarithm of both sides: x=log\u2061(64)log\u2061(9)x = \\frac{\\log(64)}{\\log(9)}x=log(9)log(64)\u200b Numerically, this will give you the answer.<\/li>\n\n\n\n
Since 10,000=10410,000 = 10^410,000=104, log\u206110(10,000)=4\\log_{10}(10,000) = 4log10\u200b(10,000)=4.<\/li>\n\n\n\n
Since 8=238 = 2^38=23, this becomes: 23x=232^{3x} = 2^323x=23 Solving for xxx, we find x=1x = 1x=1.<\/li>\n\n\n\n
Since 27=3327 = 3^327=33, log\u20613(27)=3\\log\u2083(27) = 3log3\u200b(27)=3.<\/li>\n<\/ol>\n\n\n\n
\n\n\n\n
Writing Inverses of Exponentials and Logarithms<\/h3>\n\n\n\n\n- log\u2080(x + 1)<\/strong> Inverse:<\/strong> y=x+1y = x + 1y=x+1 Explanation:<\/strong>
To find the inverse, swap xxx and yyy and solve for yyy. The result is y=x+1y = x + 1y=x+1, which is a linear function, the inverse of the logarithm.<\/li>\n\n\n\n- y = 2\u02e3<\/strong> Inverse:<\/strong> log\u20612(y)=x\\log\u2082(y) = xlog2\u200b(y)=x Explanation:<\/strong>
The inverse of an exponential function y=axy = a^xy=ax is a logarithmic function. So, to find the inverse of y=2xy = 2^xy=2x, write it as log\u20612(y)=x\\log\u2082(y) = xlog2\u200b(y)=x.<\/li>\n<\/ol>\n\n\n\n
\n\n\n\nThese examples should give you a solid understanding of the relationships between logarithmic and exponential forms.<\/p>\n\n\n\n<\/figure>\n","protected":false},"excerpt":{"rendered":"Expressing Logarithms in Exponential Form: Rewrite each logarithmic equation in exponential form. Hint: Remember the acronyms “logs are BAE” and “exponentials are B-E-A-utiful.” 1. log\u00e2\u201a\u0081(256) = 2 2. log\u00e2\u201a\u20ac\u00e2\u201a\u201e(2) = 2 3. log\u00e2\u201a\u0081\u00e2\u201a\u2021(289) 4. log\u00e1\u00b5\u00a3 Expressing Exponentials in Logarithmic Form: Rewrite each exponential equation in logarithmic form. 1. 243 = log\u00e2\u201a\u0192\u00e2\u201a\u201a\u00e2\u201a\u201e(18) 2. 7\u00e2\u0081\u00b4 = 196 […]<\/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-245880","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/245880","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=245880"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/245880\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=245880"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=245880"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=245880"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
To find the inverse, swap xxx and yyy and solve for yyy. The result is y=x+1y = x + 1y=x+1, which is a linear function, the inverse of the logarithm.<\/li>\n\n\n\n
The inverse of an exponential function y=axy = a^xy=ax is a logarithmic function. So, to find the inverse of y=2xy = 2^xy=2x, write it as log\u20612(y)=x\\log\u2082(y) = xlog2\u200b(y)=x.<\/li>\n<\/ol>\n\n\n\n
\n\n\n\n
These examples should give you a solid understanding of the relationships between logarithmic and exponential forms.<\/p>\n\n\n\n Expressing Logarithms in Exponential Form: Rewrite each logarithmic equation in exponential form. Hint: Remember the acronyms “logs are BAE” and “exponentials are B-E-A-utiful.” 1. log\u00e2\u201a\u0081(256) = 2 2. log\u00e2\u201a\u20ac\u00e2\u201a\u201e(2) = 2 3. log\u00e2\u201a\u0081\u00e2\u201a\u2021(289) 4. log\u00e1\u00b5\u00a3 Expressing Exponentials in Logarithmic Form: Rewrite each exponential equation in logarithmic form. 1. 243 = log\u00e2\u201a\u0192\u00e2\u201a\u201a\u00e2\u201a\u201e(18) 2. 7\u00e2\u0081\u00b4 = 196 […]<\/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-245880","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/245880","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=245880"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/245880\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=245880"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=245880"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=245880"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}<\/figure>\n","protected":false},"excerpt":{"rendered":"