IPMAT Indore 2024 (MCQ) - Let a = (_7 4)(_7 5 - _7 2)_7 25 (_7 8 - _7 4). Then the value of 5^a is | PYQs + Solutions

IPMAT Indore 2024

Modern Math

Logarithms

Medium

Let $a = \dfrac{(\log_7 4)(\log_7 5 - \log_7 2)}{\log_{7} 25 (\log_7 8 - \log_7 4)}$ . Then the value of $5^a$ is

\frac{5}{2}

\frac{7}{2}

Correct Option: 2

You might be wondering how

\dfrac{\log_7 \frac52}{\log_7 5} = {\log_5 \frac52}

Property used

=\boxed{ {\log_a m} = \dfrac{\log_b m}{\log_b a}}

In logarithm, you need to not just know how LHS -> RHS (in terms of the properties), but also how RHS -> LHS.