Question

$$\frac{16\times2^{n+1}-4\times2^{b}}{16\times2^{n+1}-2\times2^{n+2}}=\frac{1}{2}$$

Solve for b

$b=n+\log_{2}\left(5\right)$

Solve for n

$n=b-\log_{2}\left(5\right)$