1950 AHSME Problems/Problem 42

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Problem

The equation $x^{x^{x}}...\equal{}2$ (Error compiling LaTeX. Unknown error_msg) is satisfied when $x$ is equal to:

$\textbf{(A)}\ \infty \qquad \textbf{(B)}\ 2 \qquad \textbf{(C)}\ \sqrt[4]{2} \qquad \textbf{(D)}\ \sqrt{2} \qquad \textbf{(E)}\ \text{None of these}$