3. Positive real numbers $u, v, w$ are not equal to 1. If $\log _{u} v w+\log _{v} w=5, \log _{v} u+\log _{w} v=3$, then the value of $\log _{w} u$ is $\qquad$ .
Answer: $\frac{4}{5}$.
Solution: Let $\log _{u} v=a, \log _{v} w=b$, then
$$
\log _{v} u=\frac{1}{a}, \log _{w} v=\frac{1}{b}, \log _{u} v w=\log _{u} v+\log _{u} v \cdot \log _{v} w=a+a b,
$$

The condition becomes $a+a b+b=5, \frac{1}{a}+\frac{1}{b}=3$, from which we can get $a b=\frac{5}{4}$. Therefore,
$$
\log _{w} u=\log _{w} v \cdot \log _{v} u=\frac{1}{a b}=\frac{4}{5} .
$$