1. If the real number $x$ satisfies $\log _{2} x=\log _{4}(2 x)+\log _{8}(4 x)$, then $x=$
$$
\begin{array}{l}
\log _{2} x=\log _{4}(2 x)+\log _{8}(4 x)=\frac{1}{2} \log _{2}(2 x)+\frac{1}{3} \log _{2}(4 x)=\log _{2}\left[(2 x)^{\frac{1}{2}}(4 x)^{\frac{1}{3}}\right] \\
\Rightarrow x=(2 x)^{\frac{1}{2}}(4 x)^{\frac{1}{3}}=2^{\frac{1}{2}+\frac{2}{3}} x^{\frac{1}{2}+\frac{1}{3}}=2^{\frac{7}{6}} x^{\frac{5}{6}} \Rightarrow x=2^{7}=128 .
\end{array}
$$