{"status": "success", "data": {"description_md": "Positive real numbers $x \\neq 1$ and $y \\neq 1$ satisfy $\\log_2{x} = \\log_y{16}$ and $xy = 64$. What is $(\\log_2{\\tfrac{x}{y}})^2$?\n\n$\\textbf{(A) } \\frac{25}{2} \\qquad\\textbf{(B) } 20 \\qquad\\textbf{(C) } \\frac{45}{2} \\qquad\\textbf{(D) } 25 \\qquad\\textbf{(E) } 32$\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>Positive real numbers  <span class=\"katex--inline\">x \\neq 1</span>  and  <span class=\"katex--inline\">y \\neq 1</span>  satisfy  <span class=\"katex--inline\">\\log_2{x} = \\log_y{16}</span>  and  <span class=\"katex--inline\">xy = 64</span> . What is  <span class=\"katex--inline\">(\\log_2{\\tfrac{x}{y}})^2</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) } \\frac{25}{2} \\qquad\\textbf{(B) } 20 \\qquad\\textbf{(C) } \\frac{45}{2} \\qquad\\textbf{(D) } 25 \\qquad\\textbf{(E) } 32</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": "2019 AMC 12A Problem 12", "can_next": true, "can_prev": true, "nxt": "/problem/19_amc12A_p13", "prev": "/problem/19_amc12A_p11"}}