1. If the inequality $\log _{a} x>\tan x(a>0, a \neq 1)$ holds for any $x \in\left(0, \frac{\pi}{4}\right)$, then the range of the real number $a$ is
$\qquad$ .
Obviously, $0<a<1$, and combining with the graph, we know $\log _{a} \frac{\pi}{4} \geqslant 1=\log _{a} a \Rightarrow \frac{\pi}{4} \leqslant a<1$, so the range of the real number $a$ is $\left[\frac{\pi}{4}, 1\right)$.