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

Question and options

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

Correct answer: B - $\frac{5}{2}$

Numerator = 2log7(2)*log7(5/2); denominator = 2log7(5)*log7(2). So a = log7(5/2)/log7(5) = log5(5/2), hence 5^a = 5/2.