5. If $\log _{8} a+\log _{4} b^{2}=5$, and $\log _{8} b$ $+\log _{4} \mathrm{a}^{2}=7$. Find $\mathrm{ab}$.
Solving: Add the two equations given in the problem, and by the properties of logarithms, we get:
$$
\log _{8} a b+\log _{4} a^{2} b^{2}=12 .
$$

By changing the base, we get $\frac{\log _{2} a b}{3}+\log _{2} a b=12$,
$$
\begin{array}{l}
\frac{4}{3} \log _{2} \mathrm{ab}=12, \log _{2} \mathrm{ab}=9, \\
\therefore \mathrm{ab}=2^{9}=512 .
\end{array}
$$