Solving an equaiton which includes $log$ as both base and exponent Q:
If
$$9x = x^{\log_3x}$$
then what is $x$ ?

I can't solve it. I have tried to use identities in my book but i think they are useless for this question. I need a hint
Hint: Try taking logarithm to the base $3$ on both sides. You'll get a quadratic in $\log_3x$.
Take $\log_3$ of both sides. Then
$$ \log_3{9} + \log_3{x} = (\log_3{x}) (\log_3{x}), $$
using $\log{ab}=\log{a}+\log{b}$ and $\log{a^b} = b\log{a}$. This is a quadratic equation for $\log_3{x}$. Solve that and exponentiate $3$ with the answer to find $x$.