AHSME 1950 Problem 42

The equation $x^{x^{x^{.^{.^.}}}}=2$ is satisfied when $x$ is equal to: $\textbf{(A)}\ \infty \textbf{(B)}\ 2 \textbf{(C)}\ \sqrt[4]{2} \textbf{(D)}\ \sqrt{2} \textbf{(E)}\ \text{None of these}$