9. Let the function $f(x)=\left|2-\log _{3} x\right|$, positive real numbers $a, b, c$ satisfy $a<b<c$, and $f(a)=2 f(b)=2 f(c)$. Find the value of $\frac{a c}{b}$.
$f(x)=\left\{\begin{array}{l}2-\log _{3} x, 0<x<9, \\ \log _{3} x-2, x \geqslant 9,\end{array}\right.$ Therefore, $2-\log _{3} a=4-2 \log _{3} b=2 \log _{3} c-4$ $\Rightarrow\left\{\begin{array}{l}a c^{2}=3^{6}, \\ b c=3^{4} .\end{array}\right.$ Dividing the two equations, we get $\frac{a c}{b}=3^{2}=9$.