1. Given a real number $a>0$, and $a \neq 1$, the area of square $A B C D$ is 36, where $A B / / x$-axis, and points $A$, $B$, and $C$ are on the graphs of the functions
$$
y=\log _{a} x, y=2 \log _{a} x, y=3 \log _{a} x
$$

respectively. Then $a=$ $\qquad$ .
$-1.3^{ \pm^{\frac{1}{6}}}$.
When $a>1$, let $B\left(x_{0}, 2 \log _{a} x_{0}\right)\left(x_{0}>0\right)$. Then $A\left(x_{0}+6, \log _{a}\left(x_{0}+6\right)\right), C\left(x_{0}, 3 \log _{a} x_{0}\right)$. It is known that the side length of the square $A B C D$ is 6.
From $A B / / x$-axis, we have
$$
\left\{\begin{array}{l}
2 \log _{a} x_{0}=\log _{a}\left(x_{0}+6\right), \\
3 \log _{a} x_{0}-2 \log _{a} x_{0}=6 .
\end{array}\right.
$$

Solving this, we get $a=3^{\frac{1}{6}}$.
When $0<a<1$, similarly, we get $a=3^{-\frac{1}{6}}$.