{"status": "success", "data": {"description_md": "How many ordered pairs $(a,b)$ such that $a$ is a positive real number and $b$ is an integer between $2$ and $200$, inclusive, satisfy the equation $(\\log_b a)^{2017}=\\log_b(a^{2017})?$\n\n$\\textbf{(A)}\\ 198\\qquad\\textbf{(B)}\\ 199\\qquad\\textbf{(C)}\\ 398\\qquad\\textbf{(D)}\\ 399\\qquad\\textbf{(E)}\\ 597$\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>How many ordered pairs  <span class=\"katex--inline\">(a,b)</span>  such that  <span class=\"katex--inline\">a</span>  is a positive real number and  <span class=\"katex--inline\">b</span>  is an integer between  <span class=\"katex--inline\">2</span>  and  <span class=\"katex--inline\">200</span> , inclusive, satisfy the equation  <span class=\"katex--inline\">(\\log_b a)^{2017}=\\log_b(a^{2017})?</span> </p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 198\\qquad\\textbf{(B)}\\ 199\\qquad\\textbf{(C)}\\ 398\\qquad\\textbf{(D)}\\ 399\\qquad\\textbf{(E)}\\ 597</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": "2017 AMC 12A Problem 20", "can_next": true, "can_prev": true, "nxt": "/problem/17_amc12A_p21", "prev": "/problem/17_amc12A_p19"}}