CAT (QA) PYQs

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

If y is a negative number such that $2^{y^2log_3 5} = 5^{\log_2 3}$, then y equals

If $\log_{64} x^2 + \log_8 \sqrt{y} + 3\log_{512}\left(\sqrt{yz}\right) = 4$, where $x, y$ and $z$ are positive real numbers, then the minimum possible value of $(x+y+z)$ is