{"status": "success", "data": {"description_md": "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?\n\n$\\textbf{(A) }S<\\sqrt2 \\qquad \\textbf{(B) }S=\\sqrt2 \\qquad \\textbf{(C) }\\sqrt2<S<2\\qquad \\textbf{(D) }2\\le S<6 \\qquad \\textbf{(E) }S\\ge 6$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>Let  <span class=\"katex--inline\">S</span>  be the sum of all positive real numbers  <span class=\"katex--inline\">x</span>  for which <span class=\"katex--display\">x^{2^{\\sqrt2}}=\\sqrt2^{2^x}.</span> Which of the following statements is true?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) }S&lt;\\sqrt2 \\qquad \\textbf{(B) }S=\\sqrt2 \\qquad \\textbf{(C) }\\sqrt2&lt;S&lt;2\\qquad \\textbf{(D) }2\\le S&lt;6 \\qquad \\textbf{(E) }S\\ge 6</span> </p>&#10;<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "2021 AMC 12B Problem 21", "can_next": true, "can_prev": true, "nxt": "/problem/21_amc12B_p22", "prev": "/problem/21_amc12B_p20"}}