$\displaystyle 3\sqrt5=5^{2x}$

I thought you take the sqrt and you get $\displaystyle 5^{1/3}=5^{2x}$

Then you get $\displaystyle 5^3=5^{2x}$ So now the bases are the same and you can now solve 3=2x. Divide 2 and you get $\displaystyle x=3/2$

The answer is not that. Where did I go wrong?