IPMAT Indore (SA) PYQs

If $\log_4 x = a$ and $\log_{25} x = b$, then $\log_x 10$ is

The set of real values of $x$ for which the inequality $\log _{27} 8 \leq \log _{3} x \lt 9^{\frac{1}{\log _{2} 3}}$ holds is

If $\log_5(\log_8(x^2 - 1)) = 0$, then a possible value of $x$ is