CAT (QA) PYQs

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

Let $x$ and $y$ be positive real numbers such that $\log _{5}(x+y)+\log _{5}(x-y)=3$, and $\log _{2} y-\log _{2} x=1-\log _{2} 3$. Then $x y$ equals