IPMAT Indore 2019 (SA) PYQs

The inequality $\log_{2} \frac{3x - 1}{2 - x} < 1$ holds true for

Let $a, b, c$ be real numbers greater than 1, and $n$ be a positive real number not equal to 1. If $log_n(log_2a) = 1; log_n(log_2b) = 2$ and $log_n(log_2c) = 3$ then which of the following is true?

If $\log_{(cos x)}(sin x) + \log_{(sin x)}(cos x) = 2,$ then the value of $x$ is