What properties of exponents and logarithms is used here?

Question

In a solution to one of my assignment is given that:

$$4^{log_{16} n} = n^{log_{16} 4} = n^{\frac12}$$

I understand the 2nd part, that's simple, but how was the first part achieved?

Answer 1

Let $$y=4^{\log_{16}x}$$ $$\log_{16}y=\log_{16}(x^{\log_{16}4})$$ $$\log_{16}y=\log_{16}(x^{1/2})$$ $$y=x^{1/2}$$

Answer 2

Indeed an important part is missing:

$4^{log_{16}n}= 16^{log_{16}4*log_{16}n} = n^{log_{16}4} $