CAT (QA) PYQs

If $x$ is a real number such that $\log_3 5 = \log_5 (2 + x)$, then which of the following is true?

The sum of all possible real values of $x$ for which $\log_{x-3}(x^2-9)=\log_{x-3}(x+1)+2$, is

The number of distinct integer values of n satisfying $\frac{4-\log_2 n}{3-\log_4 n} < 0$, is