CAT (QA) PYQs

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

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

For a real number $a$, if $\frac{\log _{15} a+\log _{32} a}{\left(\log _{15} a\right)\left(\log _{32} a\right)}=4$ then a must lie in the range.