{"status": "success", "data": {"description_md": "Let $m>1$ and $n>1$ be integers. Suppose that the product of the solutions for $x$ of the equation\n\n$$8(\\log_n x)(\\log_m x)-7\\log_n x-6 \\log_m x-2013 = 0$$<br>is the smallest possible integer. What is $m+n$?\n\n$\\textbf{(A)}\\ 12\\qquad\\textbf{(B)}\\ 20\\qquad\\textbf{(C)}\\ 24\\qquad\\textbf{(D)}\\ 48\\qquad\\textbf{(E)}\\ 272$\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\">m&gt;1</span>  and  <span class=\"katex--inline\">n&gt;1</span>  be integers. Suppose that the product of the solutions for  <span class=\"katex--inline\">x</span>  of the equation</p>&#10;<p> <span class=\"katex--display\">8(\\log_n x)(\\log_m x)-7\\log_n x-6 \\log_m x-2013 = 0</span> <br/>is the smallest possible integer. What is  <span class=\"katex--inline\">m+n</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 12\\qquad\\textbf{(B)}\\ 20\\qquad\\textbf{(C)}\\ 24\\qquad\\textbf{(D)}\\ 48\\qquad\\textbf{(E)}\\ 272</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": "2013 AMC 12B Problem 22", "can_next": true, "can_prev": true, "nxt": "/problem/13_amc12B_p23", "prev": "/problem/13_amc12B_p21"}}