3. Let the function $f(x)=\log _{a} \frac{x-2 a}{x+2 a}(a>0$, and $a \neq 1)$, if $x \in[s, t]$, then $f(x) \in\left[\log _{a}(t-a)\right.$, $\left.\log _{u}(s-a)\right]$, find the range of real number $a$.
3. From the problem, $\left\{\begin{array}{l}\frac{x-2 a}{x+2 a}>0 \\ t-a>0 \\ s-a>0\end{array} \Rightarrow\left\{\begin{array}{l}x>2 a, xa \\ s>a\end{array}\right.\right.$ Also, since $x \in[s, t]$, we know: $x>2 a$ which means we consider $(2 a,+\infty)$; From $t-a>s-a>0$ and $\log _{a}(t-a)2 a \\ \Delta>0 \\ h(2 a)>0\end{array} \Rightarrow\left\{a \left\lvert\, 0<a<\frac{1}{a}\right.\right\}\right.$ is the solution.