Answer
$x\in\{1, 10^{-\sqrt{3}}, 10^{\sqrt{3}}\}$
Work Step by Step
Let $t=\log x$
The equation becomes
$t^{3}=3t$
$t^{3}-3t=0$
$t(t^{2}-3)=0$
...the parentheses can be factored as a difference of squares...
$t(t-\sqrt{3})(t+\sqrt{3})=0$
Solutions:
$\left[\begin{array}{lll}
t=0 & t=-\sqrt{3} & t=\sqrt{3}\\
\log x=0 & \log x=-\sqrt{3} & \log x=\sqrt{3}\\
x=1 & x=10^{-\sqrt{3}} & x=10^{\sqrt{3}}
\end{array}\right]$
$x\in\{1, 10^{-\sqrt{3}}, 10^{\sqrt{3}}\}$
