Transform $2^{2\log n}$, given that $\log$ is base 10, to $n^{2/\log_2 10}$

Question

Can anyone show me the step by step transformation? This is the answer given in a class but I'm getting tripped up over here. Thank you.

Answer 1

Note that \begin{eqnarray} n^{\frac{2}{\log_{2}{10}}}&=&n^{\frac{\log_{2} 2^2}{\log_{2}{10}}}=n^{\log 2^2}=2^{\log_{2}{n^{\log 2^2}}}=2^{\log 2^2\log_2{n}}=2^{2\log 2\log_2{n}}=2^{2\log 2\frac{\log{n}}{\log 2}}=2^{2\log{n}} \end{eqnarray}