Find $\log _{3 / 2} 3.375$

If $\log x : 3 = \log y : 4 = \log z : 5$,then $zx =$

If $y = \frac{1}{a^{1-\log _{a} x}}$,$z = \frac{1}{a^{1-\log _{a} y}}$ and $x = a^{k}$,then $k =$

If $\log _{2} x+\log _{4} x+\log _{16} x=21 / 4,$ then $x=$

If $4^{x} + 2^{2x-1} = 3^{x+\frac{1}{2}} + 3^{x-\frac{1}{2}},$ then $x =$

$\log _{5}\left(1+\frac{1}{5}\right)+\log _{5}\left(1+\frac{1}{6}\right)+\log _{5}\left(1+\frac{1}{7}\right)+\cdots+\log _{5} \left(1+\frac{1}{624}\right)$