Solving ${\sqrt2}^{\,x} = {\sqrt3}^{\,x}$ I am studying logarithms and exponents.  I am not sure how to go about solving this problem.  I seem too keep going in circles using the rules of log and exp.
$$(\sqrt{2})^x = (\sqrt{3})^x$$

Maybe the quickest way is to divide both sides by $\sqrt2^x$. Then you get $1=\sqrt{3/2}^x$, and you know that for a number $a>1$, the only power $a^x$ that’s equal to $1$ is for $x=0$.
