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, $a \neq 1$.
[Solution] $\log _{a}\left[\left(\frac{m^{4} n^{-4}}{m^{-1} n}\right)^{-3} \div\left(\frac{m^{-2} n^{2}}{m n^{-1}}\right)^{5}\right]$
$$
\begin{array}{l}
=\log _{a}\left[\left(m^{5} n^{-5}\right)^{-3} \div\left(m^{-3} n^{3}\right)^{5}\right] \\
=\log _{a}\left(m^{-15} n^{15} \div m^{-15} n^{15}\right) \\
=\log _{a} 1 \\
=0
\end{array}
$$