{"status": "success", "data": {"description_md": "The solution to the equation $\\log_{3x} 4 = \\log_{2x} 8$, where $x$ is a positive real number other than $\\frac{1}{3}$ or $\\frac{1}{2}$, can be written as $\\frac {p}{q}$ where $p$ and $q$ are relatively prime positive integers. What is $p + q$?\n\n$\\textbf{(A) } 5   \\qquad    <br>\\textbf{(B) } 13   \\qquad    <br>\\textbf{(C) } 17   \\qquad   <br>\\textbf{(D) } 31 \\qquad  <br>\\textbf{(E) } 35$\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 solution to the equation  <span class=\"katex--inline\">\\log_{3x} 4 = \\log_{2x} 8</span> , where  <span class=\"katex--inline\">x</span>  is a positive real number other than  <span class=\"katex--inline\">\\frac{1}{3}</span>  or  <span class=\"katex--inline\">\\frac{1}{2}</span> , can be written as  <span class=\"katex--inline\">\\frac {p}{q}</span>  where  <span class=\"katex--inline\">p</span>  and  <span class=\"katex--inline\">q</span>  are relatively prime positive integers. What is  <span class=\"katex--inline\">p + q</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) } 5   \\qquad    \\textbf{(B) } 13   \\qquad    \\textbf{(C) } 17   \\qquad   \\textbf{(D) } 31 \\qquad  \\textbf{(E) } 35</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": "2018 AMC 12A Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/18_amc12A_p15", "prev": "/problem/18_amc12A_p13"}}