AMC 12 2005a Problem 23

Two distinct numbers $a$ and $b$ are chosen randomly from the set $\{2, 2^2, 2^3, \ldots, 2^{25}\}$. What is the probability that $\log_{a}b$ is an integer?

$\textbf{(A) } \frac{2}{25} \textbf{(B) } \frac{31}{300} \textbf{(C) } \frac{13}{100} \textbf{(D) } \frac{7}{50} \textbf{(E) } \frac{1}{2}$