$9 \cdot 13$ If $\left(\log _{2} 3\right)^{x}-\left(\log _{5} 3\right)^{x} \geqslant\left(\log _{2} 3\right)^{-y}-\left(\log _{5} 3\right)^{-y}$, then
(A) $x-y \geqslant 0$
(B) $x+y \geqslant 0$
(C) $x-y \leqslant 0$
(D) $x+y \leqslant 0$
(China High School Mathematics League, 1999)
[Solution] Let $f(t)=\left(\log _{2} 3\right)^{t}-\left(\log _{5} 3\right)^{t}$, then $f(t)$ is a strictly increasing function on the real number domain $R$.
The original inequality is $f(x) \geqslant f(-y)$, hence $x \geqslant -y$, which means $x+y \geqslant 0$. Therefore, the answer is $(B)$.