2003 AMC 10B Problem 9

Find the value of x that satisfies the equation 25^{-2} = \frac{5^{48/x}}{5^{26/x} \cdot 25^{17/x}}.

\textbf{(A) } 2 \qquad\textbf{(B) } 3 \qquad\textbf{(C) } 5 \qquad\textbf{(D) } 6 \qquad\textbf{(E) } 9

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.