Solve for x:

x = $\dfrac{\text{log 125}}{\text{log 25}}$

Solve for x:

$\dfrac{\text{log 8}}{\text{log 2}} \times \dfrac{\text{log 3}}{\text{log}\sqrt{3}} = 2\text{log} x$

If $\dfrac{\text{log x}}{\text{log 5}} = \dfrac{\text{log y}^2}{\text{log 2}} = \dfrac{\text{log 9}}{\text{log}\dfrac{1}{3}}$, find x and y.

Prove the following:

3^{log 4} = 4^{log 3}