AMC 12 2019a Problem 12

Positive real numbers $x \neq 1$ and $y \neq 1$ satisfy $\log_2{x} = \log_y{16}$ and $xy = 64$. What is $(\log_2{\tfrac{x}{y}})^2$?

$\textbf{(A) } \frac{25}{2} \textbf{(B) } 20 \textbf{(C) } \frac{45}{2} \textbf{(D) } 25 \textbf{(E) } 32$