3・1 Simplify:
$$\log _{a}\left[\left(\frac{m^{4} n^{-4}}{m^{-1} n}\right)^{-3} \div\left(\frac{m^{-2} n^{2}}{m n^{-1}}\right)^{5}\right]$$

Here $m$, $n$, and $a$ are all positive numbers, $a \neq 1$.