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Algebra Level 2

25 log ⁡ 5 99 = ? \large { 25 }^{\log _{ 5 }{ 99 } } = \, ?


The answer is 9801.

Aniket Sanghi by Aniket Sanghi , 21, India

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4 solutions

By using the identity b log ⁡ b x = x b^{\log_{b}x} = x

2 5 log ⁡ 5 99 = 5 log ⁡ 5 9 9 2 = 9 9 2 = 9801 \large \begin{aligned} 25^{\log_{5}99} &= 5^{\log_{5}99^2} \\& = 99^2 \\& = 9801 \boxed{} \end{aligned}

F I N ! ! ! \LARGE \ce{FIN!!!}

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Abhiram Rao
Mar 26, 2016

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Kamalpreet Singh
Feb 1, 2016

The given expression gives : 99^2 =9801

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Aniket Sanghi
Feb 1, 2016

use identity a log ⁡ a b = b { a }^{\log _{ a }{ b } } = b

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