CAT (QA) PYQs

Suppose, $\log_3 x = \log_{12} y = a$, where $x, y$ are positive numbers. If $G$ is the geometric mean of x and y, and $\log_6 G$ is equal to

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 value of $\log_a \left(\frac{a}{b}\right) + \log_b \left(\frac{b}{a}\right)$, for $1 < a \leq b$ cannot be equal to