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?

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

If $\log _{2}\left(5+\log _{3} a\right)=3$ and $\log _{5}\left(4 a+12+\log _{2} b\right)=3$, then $a+b$ is equal to