Question

The value of 'a' for which $\frac{{\log }_{a}7}{{\log }_{6}7}={\log }_{\pi }36$ holds good, is

• A. $1/\pi$
• B. ${\pi }^2$
• C. $\sqrt{\pi }$
• D. 2

Answer 1

Answer: (C)

${\log }_{a}7\cdot {\log }_{7}6={\log }_{\pi }36$
${\log }_{a}6=2{\log }_{\pi }6=\frac{{\log }_{\pi }6}{{\log }_{\pi }a}=2{\log }_{\pi }6\Rightarrow {\log }_{\pi }a=\frac{1}{2}\Rightarrow a=\sqrt{\pi }$