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

If $x$ and $y$ are positive real numbers such that $\log_{x}\left(x^{2}+12\right)=4$ and $3 \log _{y} x=1$, then $x+y$ equals