3. Let positive real numbers $u, v, w$ be 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
3. $\frac{4}{5}$.

Let $\log _{u} v=a, \log _{v} w=b$. Then
$$
\begin{array}{l}
\log _{v} u=\frac{1}{a}, \log _{w} v=\frac{1}{b}, \\
\log _{u} v w=\log _{u} v+\left(\log _{u} v\right)\left(\log _{v} w\right)=a+a b .
\end{array}
$$

Therefore, $a+a b+b=5, \frac{1}{a}+\frac{1}{b}=3$
$$
\Rightarrow a b=\frac{5}{4} \text {. }
$$

Thus, $\log _{w} u=\left(\log _{w} v\right)\left(\log _{v} u\right)=\frac{1}{a b}=\frac{4}{5}$.