{"status": "success", "data": {"description_md": "[[Square]] $ABCD$ has area $36,$ and $\\overline{AB}$ is [[parallel]] to the [[x-axis]]. Vertices $A,$ $B$, and $C$ are on the graphs of $y = \\log_{a}x,$ $y = 2\\log_{a}x,$ and $y = 3\\log_{a}x,$ respectively. What is $a?$<br>\t\n\n$\\mathrm{(A)}\\ \\sqrt [6]{3}\\qquad \\mathrm{(B)}\\ \\sqrt {3}\\qquad \\mathrm{(C)}\\ \\sqrt [3]{6}\\qquad \\mathrm{(D)}\\ \\sqrt {6}\\qquad \\mathrm{(E)}\\ 6$\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>[[Square]]  <span class=\"katex--inline\">ABCD</span>  has area  <span class=\"katex--inline\">36,</span>  and  <span class=\"katex--inline\">\\overline{AB}</span>  is [[parallel]] to the [[x-axis]]. Vertices  <span class=\"katex--inline\">A,</span>   <span class=\"katex--inline\">B</span> , and  <span class=\"katex--inline\">C</span>  are on the graphs of  <span class=\"katex--inline\">y = \\log_{a}x,</span>   <span class=\"katex--inline\">y = 2\\log_{a}x,</span>  and  <span class=\"katex--inline\">y = 3\\log_{a}x,</span>  respectively. What is  <span class=\"katex--inline\">a?</span> <br/></p>&#10;<p> <span class=\"katex--inline\">\\mathrm{(A)}\\ \\sqrt [6]{3}\\qquad \\mathrm{(B)}\\ \\sqrt {3}\\qquad \\mathrm{(C)}\\ \\sqrt [3]{6}\\qquad \\mathrm{(D)}\\ \\sqrt {6}\\qquad \\mathrm{(E)}\\ 6</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": "2007 AMC 12A Problem 23", "can_next": true, "can_prev": true, "nxt": "/problem/07_amc12A_p24", "prev": "/problem/07_amc12A_p22"}}