{"status": "success", "data": {"description_md": "The domain of the function $f(x)=\\log_{\\frac12}(\\log_4(\\log_{\\frac14}(\\log_{16}(\\log_{\\frac1{16}}x))))$ is an interval of length $\\tfrac mn$, where $m$ and $n$ are relatively prime positive integers.  What is $m+n$?\n\n$\\textbf{(A) }19\\qquad<br>\\textbf{(B) }31\\qquad<br>\\textbf{(C) }271\\qquad<br>\\textbf{(D) }319\\qquad<br>\\textbf{(E) }511\\qquad$\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>The domain of the function  <span class=\"katex--inline\">f(x)=\\log_{\\frac12}(\\log_4(\\log_{\\frac14}(\\log_{16}(\\log_{\\frac1{16}}x))))</span>  is an interval of length  <span class=\"katex--inline\">\\tfrac mn</span> , where  <span class=\"katex--inline\">m</span>  and  <span class=\"katex--inline\">n</span>  are relatively prime positive integers.  What is  <span class=\"katex--inline\">m+n</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) }19\\qquad\\textbf{(B) }31\\qquad\\textbf{(C) }271\\qquad\\textbf{(D) }319\\qquad\\textbf{(E) }511\\qquad</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": "2014 AMC 12A Problem 18", "can_next": true, "can_prev": true, "nxt": "/problem/14_amc12A_p19", "prev": "/problem/14_amc12A_p17"}}