Question

$$\quad \log _ { 3 } U \times \log _ { 2 } N \times \log _ { 3 } M = 1$$

Solve for M

$M=3^{\frac{8^{\frac{1}{U}}}{N}}$
$N\neq 0\text{ and }U\neq 0$

Solve for N

$N=\log_{M}\left(3\right)\times 8^{\frac{1}{U}}$
$\left(U>0\text{ and }M>M^{8^{-\frac{1}{U}}}\text{ and }M>1\right)\text{ or }\left(M>0\text{ and }M0\right)\text{ or }\left(M<1\text{ and }U<0\text{ and }M>M^{8^{-\frac{1}{U}}}\text{ and }M>0\right)\text{ or }\left(M1\right)$