How to show that $ n^{2} = 4^{{\log_{2}}(n)} $? I ran across this simple identity yesterday, but can’t seem to find a way to get from one side to the other:
$$
n^{2} = 4^{{\log_{2}}(n)}.
$$
Wolfram Alpha tells me that it is true, but other than that, I’m stuck.

Take $\log_{2}$ of both sides and get
$$n^{2} = 4^{{\log_{2}} n}$$
$$2\log_{2}n =2\log_{2}n $$
