{"status": "success", "data": {"description_md": "Suppose $x$ and $y$ are positive real numbers such that\n\n$$x^y=2^{64}\\text{ and }(\\log_2{x})^{\\log_2{y}}=2^{7}.$$<br>What is the greatest possible value of $\\log_2{y}$?\n\n$\\textbf{(A) }3 \\qquad \\textbf{(B) }4 \\qquad \\textbf{(C) }3+\\sqrt{2} \\qquad \\textbf{(D) }4+\\sqrt{3} \\qquad \\textbf{(E) }7$\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>Suppose  <span class=\"katex--inline\">x</span>  and  <span class=\"katex--inline\">y</span>  are positive real numbers such that</p>&#10;<p> <span class=\"katex--display\">x^y=2^{64}\\text{ and }(\\log_2{x})^{\\log_2{y}}=2^{7}.</span> <br/>What is the greatest possible value of  <span class=\"katex--inline\">\\log_2{y}</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) }3 \\qquad \\textbf{(B) }4 \\qquad \\textbf{(C) }3+\\sqrt{2} \\qquad \\textbf{(D) }4+\\sqrt{3} \\qquad \\textbf{(E) }7</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": 3, "problem_name": "2022 AMC 12B Problem 16", "can_next": true, "can_prev": true, "nxt": "/problem/22_amc12B_p17", "prev": "/problem/22_amc12B_p15"}}