{"status": "success", "data": {"description_md": "The graphs of $y=\\log_3 x, y=\\log_x 3, y=\\log_\\frac{1}{3} x,$ and $y=\\log_x \\dfrac{1}{3}$ are plotted on the same set of axes. How many points in the plane with positive $x$-coordinates lie on two or more of the graphs? \n\n$\\textbf{(A)}\\ 2\\qquad\\textbf{(B)}\\ 3\\qquad\\textbf{(C)}\\ 4\\qquad\\textbf{(D)}\\ 5\\qquad\\textbf{(E)}\\ 6$\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>The graphs of  <span class=\"katex--inline\">y=\\log_3 x, y=\\log_x 3, y=\\log_\\frac{1}{3} x,</span>  and  <span class=\"katex--inline\">y=\\log_x \\dfrac{1}{3}</span>  are plotted on the same set of axes. How many points in the plane with positive  <span class=\"katex--inline\">x</span> -coordinates lie on two or more of the graphs?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 2\\qquad\\textbf{(B)}\\ 3\\qquad\\textbf{(C)}\\ 4\\qquad\\textbf{(D)}\\ 5\\qquad\\textbf{(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": 3, "problem_name": "2016 AMC 12A Problem 16", "can_next": true, "can_prev": true, "nxt": "/problem/16_amc12A_p17", "prev": "/problem/16_amc12A_p15"}}