# 2021 AMC 12B Problems/Problem 21

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## Problem

Let $S$ be the sum of all positive real numbers $x$ for which$$x^{2^{\sqrt2}}=\sqrt2^{2^x}.$$Which of the following statements is true?

$\textbf{(A) }S<\sqrt2 \qquad \textbf{(B) }S=\sqrt2 \qquad \textbf{(C) }\sqrt2