Question

$$\log _ { 9 } U \times \log _ { 2 } V \times \log _ { 3 } M = 1$$

Solve for M

$M=3^{\frac{512^{\frac{1}{U}}}{V}}$
$V\neq 0\text{ and }U\neq 0$

Solve for U

$U=\frac{9\ln(2)}{\ln(V\ln(M))-\ln(\ln(3))}$
$\left(V<0\text{ and }M<1\text{ and }M>0\text{ and }V\neq \log_{M}\left(3\right)\right)\text{ or }\left(V>0\text{ and }M>1\text{ and }V\neq \log_{M}\left(3\right)\right)$