AMC 12 2005b Problem 13

Suppose that $4^{x_1}=5$, $5^{x_2}=6$, $6^{x_3}=7$, $\ldots$, $127^{x_{124}}=128$. What is $x_1x_2\cdots x_{124}$?

\textbf{(A)}\ 2 \textbf{(B)}\ \frac{5}{2} \textbf{(C)}\ 3 \textbf{(D)}\ \frac{7}{2} \textbf{(E)}\ 4