{"id":39095,"date":"2025-06-26T19:55:14","date_gmt":"2025-06-26T19:55:14","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=39095"},"modified":"2025-06-26T19:55:16","modified_gmt":"2025-06-26T19:55:16","slug":"which-of-the-following-equations-is-equivalent-to-25x-7","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/which-of-the-following-equations-is-equivalent-to-25x-7\/","title":{"rendered":"Which of the following equations is equivalent to 25x = 7"},"content":{"rendered":"\n

Which of the following equations is equivalent to 25x = 7? A. x = log2(3) + 1 + 9 = 3? B. x = log27(5) C. x = log2(5) + log5 D. x = 2<\/p>\n\n\n\n

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

We are given the equation:<\/p>\n\n\n\n

25^x = 7<\/strong><\/p>\n\n\n\n

We are asked to find which of the given choices is equivalent to this equation. To solve this, we need to isolate x<\/strong> using logarithms.<\/p>\n\n\n\n

\n\n\n\n

Step 1: Take logarithms on both sides<\/h3>\n\n\n\n

Take the logarithm base 10 (or natural logarithm) of both sides:log\u2061(25x)=log\u2061(7)\\log(25^x) = \\log(7)log(25x)=log(7)<\/p>\n\n\n\n

Apply the logarithmic rule:log\u2061(ab)=b\u22c5log\u2061(a)\\log(a^b) = b \\cdot \\log(a)log(ab)=b\u22c5log(a)x\u22c5log\u2061(25)=log\u2061(7)x \\cdot \\log(25) = \\log(7)x\u22c5log(25)=log(7)<\/p>\n\n\n\n

\n\n\n\n

Step 2: Solve for x<\/h3>\n\n\n\n

x=log\u2061(7)log\u2061(25)x = \\frac{\\log(7)}{\\log(25)}x=log(25)log(7)\u200b<\/p>\n\n\n\n

Now, express 25 as 525^252. So:log\u2061(25)=log\u2061(52)=2\u22c5log\u2061(5)\\log(25) = \\log(5^2) = 2 \\cdot \\log(5)log(25)=log(52)=2\u22c5log(5)<\/p>\n\n\n\n

Thus:x=log\u2061(7)2\u22c5log\u2061(5)x = \\frac{\\log(7)}{2 \\cdot \\log(5)}x=2\u22c5log(5)log(7)\u200b<\/p>\n\n\n\n

This expression is equal to:x=12\u22c5log\u2061(7)log\u2061(5)=12\u22c5log\u20615(7)x = \\frac{1}{2} \\cdot \\frac{\\log(7)}{\\log(5)} = \\frac{1}{2} \\cdot \\log_5(7)x=21\u200b\u22c5log(5)log(7)\u200b=21\u200b\u22c5log5\u200b(7)<\/p>\n\n\n\n

This is not<\/strong> directly shown in any of the answer choices, so let\u2019s analyze each:<\/p>\n\n\n\n

\n\n\n\n

Evaluate the Choices:<\/h3>\n\n\n\n

A.<\/strong> x = log\u2082(3) + 1 + 9 = 3 \u2192 This is incorrect and does not relate logically to the original equation.<\/p>\n\n\n\n

B.<\/strong> x = log\u2082\u2087(5)
This means:27x=527^x = 527x=5<\/p>\n\n\n\n

But the original equation is:25x=725^x = 725x=7<\/p>\n\n\n\n

These bases and results are different. So this is incorrect<\/strong>.<\/p>\n\n\n\n

C.<\/strong> x = log\u2082(5) + log(5)
This is an invalid expression because log\u2082(5) and log(5) are not equal or combinable directly. Also, nothing connects it to the equation 25^x = 7. Incorrect<\/strong>.<\/p>\n\n\n\n

D.<\/strong> x = 2
Let\u2019s test:252=625\u2260725^2 = 625 \\neq 7252=625\ue020=7<\/p>\n\n\n\n

So incorrect<\/strong>.<\/p>\n\n\n\n

\n\n\n\n

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

None<\/strong> of the options are correct. However, if forced to choose the closest match, none correctly simplify to x=log\u2061(7)log\u2061(25)x = \\frac{\\log(7)}{\\log(25)}x=log(25)log(7)\u200b.<\/p>\n\n\n\n

So, the accurate value of x<\/strong> from 25x=725^x = 725x=7 is:x=log\u2061(7)log\u2061(25)x = \\frac{\\log(7)}{\\log(25)}x=log(25)log(7)\u200b<\/p>\n\n\n\n

Or:x=log\u206125(7)x = \\log_{25}(7)x=log25\u200b(7)<\/p>\n\n\n\n

This is the correct equivalent equation.<\/p>\n\n\n\n

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

Which of the following equations is equivalent to 25x = 7? A. x = log2(3) + 1 + 9 = 3? B. x = log27(5) C. x = log2(5) + log5 D. x = 2 The Correct Answer and Explanation is: We are given the equation: 25^x = 7 We are asked to find which […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-39095","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/39095","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=39095"}],"version-history":[{"count":2,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/39095\/revisions"}],"predecessor-version":[{"id":39098,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/39095\/revisions\/39098"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=39095"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=39095"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=39095"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}