13. [9] Suppose $x, y$, and $z$ are real numbers greater than 1 such that
$$
\begin{aligned}
x^{\log _{y} z} & =2, \\
y^{\log _{y} x} & =4, \text { and } \\
z^{\log _{x} y} & =8 .
\end{aligned}
$$

Compute $\log _{x} y$.