10. 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 $\frac{a c}{b}$.
$$
\begin{array}{l}
f(x)=\left\{\begin{array}{l}
2-\log _{3} x, 0<x<9, \\
\log _{3} x-2, x \geqslant 9,
\end{array} \text {, so we have } 2-\log _{3} a=4-2 \log _{3} b=2 \log _{3} c-4\right. \\
\Rightarrow\left\{\begin{array}{l}
a c^{2}=3^{6}, \\
b c=3^{4} .
\end{array} \text { Dividing the two equations, we get } \frac{a c}{b}=3^{2}=9 .\right.
\end{array}
$$