{"id":273504,"date":"2025-07-27T13:56:46","date_gmt":"2025-07-27T13:56:46","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=273504"},"modified":"2025-07-27T13:56:49","modified_gmt":"2025-07-27T13:56:49","slug":"solve-the-equation-5","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/27\/solve-the-equation-5\/","title":{"rendered":"Solve the equation.\u00a0"},"content":{"rendered":"\n
\"\"<\/figure>\n\n\n\n

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

w \u2248 36.680<\/strong><\/p>\n\n\n\n

To solve the equation 160 \u22c5 1.075^w = 250 \u22c5 1.062^w, we need to isolate the variable w<\/em>, which is in the exponent. This requires using logarithms.<\/p>\n\n\n\n

First, we rearrange the equation to group the terms with the variable w<\/em> on one side and the constant terms on the other. We can do this by dividing both sides by 160 and also dividing both sides by 1.062^w.<\/p>\n\n\n\n

Start with the original equation:
160 \u22c5 1.075^w = 250 \u22c5 1.062^w<\/p>\n\n\n\n

Divide both sides by 1.062^w:
160 \u22c5 (1.075^w \/ 1.062^w) = 250<\/p>\n\n\n\n

Divide both sides by 160:
(1.075^w \/ 1.062^w) = 250 \/ 160<\/p>\n\n\n\n

Next, we simplify both sides. On the left, we use the exponent property (a^x \/ b^x) = (a\/b)^x. On the right, we simplify the fraction.
(1.075 \/ 1.062)^w = 1.5625<\/p>\n\n\n\n

To solve for the exponent w<\/em>, we take the natural logarithm (ln) of both sides of the equation.
ln[(1.075 \/ 1.062)^w] = ln(1.5625)<\/p>\n\n\n\n

Using the power rule of logarithms, which is ln(a^b) = b \u22c5 ln(a), we can move the exponent w<\/em> to the front as a coefficient:
w<\/em> \u22c5 ln(1.075 \/ 1.062) = ln(1.5625)<\/p>\n\n\n\n

Finally, to isolate w<\/em>, we divide both sides by ln(1.075 \/ 1.062):
w<\/em> = ln(1.5625) \/ ln(1.075 \/ 1.062)<\/p>\n\n\n\n

Now, we use a calculator to find the numerical value:
w<\/em> \u2248 0.4462871 \/ 0.0121668
w<\/em> \u2248 36.68007…<\/p>\n\n\n\n

The problem requires the answer to be rounded to three decimal places. The fourth decimal place is 0, so we round down.<\/p>\n\n\n\n

Therefore, w<\/em> \u2248 36.680.<\/p>\n\n\n\n

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

The Correct Answer and Explanation is: w \u2248 36.680 To solve the equation 160 \u22c5 1.075^w = 250 \u22c5 1.062^w, we need to isolate the variable w, which is in the exponent. This requires using logarithms. First, we rearrange the equation to group the terms with the variable w on one side and the constant terms on the […]<\/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-273504","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/273504","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=273504"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/273504\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=273504"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=273504"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=273504"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}