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.

Let $n=2^t$ then for LHS we have : $n^2=(2^t)^2=2^{2t}$
and for RHS : $4^{Log_2 n}=4^{Log_2 2^t}=4^t=(2^2)^t=2^{2t}$
LHS = RHS $\square$
