1. In the geometric sequence $\left\{a_{n}\right\}$, $a_{9}=13, a_{13}=1$, then the value of $\log _{a_{1}} 13$ is $\qquad$ .
Consider the geometric sequence: $a_{1}, a_{5}, a_{9}, a_{13}$, since $a_{13}=1, a_{9}=13$, then $a_{5}=13^{2}, a_{1}=13^{3}$. Therefore, $\log _{a_{1}} 13=\log _{13^{3}} 13=\frac{1}{3}$.