1. Solve the inequality
$$
(\sqrt{3}-\sqrt{2})^{\left(\log _{2} 3\right)^{4-x^{2}}} \leqslant(\sqrt{3}+\sqrt{2})^{-\left(\log _{3} 2\right)^{2 x-1}} \text {. }
$$
1. Notice,
$$
\begin{array}{l}
(\sqrt{3}-\sqrt{2})^{\left(\log _{2} 3\right)^{4-x^{2}}} \leqslant(\sqrt{3}+\sqrt{2})^{-\left(\log _{3} 2\right) 2 x-1} \\
\Leftrightarrow a^{\left(\log _{2} 3\right)^{4-x^{2}}} \leqslant a^{\left(\log _{3} 2\right) 2 x-1},
\end{array}
$$

where, $a=\sqrt{3}-\sqrt{2}=(\sqrt{3}+\sqrt{2})^{-1}1$.
$$
\begin{array}{l}
\text { Hence, equation (2) } \Leftrightarrow 4-x^{2} \geqslant 1-2 x \\
\Leftrightarrow(x+1)(x-3) \leqslant 0 \\
\Leftrightarrow-1 \leqslant x \leqslant 3 .
\end{array}
$$