Answer
$x=6$
Work Step by Step
Given: $\log_3 x=\log_9 6x\\\log_3x=\frac{\log_3 6x}{\log_3 9}\\\log_3 x=\frac{\log_3 6x}{2}\\2\log_3x=\log_3 6x\\\log_3x^2=\log_3 6x\\x^2=6x\\x^2-6x=0\\x(x-6)=0\\x=0 \lor x=6$
Since $x$ can't be in the original equation, the only solution is $x=6$.
