1. The positive numbers $b_{1}, b_{2}, \cdots, b_{60}$ are arranged in sequence and satisfy $\frac{b_{2}}{b_{1}}=\frac{b_{3}}{b_{2}}=\cdots=\frac{b_{60}}{b_{59}}$.
Determine the value of $\log _{b_{11} b_{50}}\left(b_{1} b_{2} \cdots b_{60}\right)$.
Given that $\left\{b_{k}\right\}$ is a geometric sequence with a common ratio of $q$, then $b_{k}=b_{1} q^{k-1}$. Therefore, $b_{k} b_{61-k}=b_{1} b_{60}$. Hence,
$$
\begin{array}{l}
\log _{b_{11} b_{50}}\left(b_{1} b_{2} \cdots b_{60}\right) \\
=\log _{b_{1} b_{60}}\left(b_{1} b_{60}\right)^{30}=30 .
\end{array}
$$