$\log_2(x) = \log_x(2) $
Using the change of base theorem: $\dfrac{\log(x)}{\log(2)} = \dfrac{\log(2)}{\log(x)}$
Multiplied the denominators on both sides: $\log(x)\log(x) = \log(2)\log(2)$
I kind of get stuck here. I know that you can't take the square root of both sides of the equation, but still, $x = 2$ seems to be an obvious solution to the equation. I've missed $2^{-1}$ or $\frac12$ as another answer to the equation, which I am struggling to get to.
Any help will be greatly appreciated, thanks in advance.