{"status": "success", "data": {"description_md": "What is the product of all the solutions to the equation $$\\log_{7x}2023 \\cdot \\log_{289x} 2023 = \\log_{2023x} 2023?$$\n\n$\\textbf{(A) }(\\log_{2023}7 \\cdot \\log_{2023}289)^2 \n\\qquad$\n$\\textbf{(B) }\\log_{2023}7 \\cdot \\log_{2023}289 \\qquad\\textbf{(C) } 1$<br>$\\textbf{(D) }\\log_{7}2023 \\cdot \\log_{289}2023\\qquad\\textbf{(E) }(\\log_{7}2023 \\cdot \\log_{289}2023)^2$\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>What is the product of all the solutions to the equation <span class=\"katex--display\">\\log_{7x}2023 \\cdot \\log_{289x} 2023 = \\log_{2023x} 2023?</span></p>&#10;<p><span class=\"katex--inline\">\\textbf{(A) }(\\log_{2023}7 \\cdot \\log_{2023}289)^2 &#10;\\qquad</span><br/>&#10;<span class=\"katex--inline\">\\textbf{(B) }\\log_{2023}7 \\cdot \\log_{2023}289 \\qquad\\textbf{(C) } 1</span><br/><span class=\"katex--inline\">\\textbf{(D) }\\log_{7}2023 \\cdot \\log_{289}2023\\qquad\\textbf{(E) }(\\log_{7}2023 \\cdot \\log_{289}2023)^2</span></p>&#10;<hr/>&#10;<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>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2023 AMC 12A Problem 19", "can_next": true, "can_prev": true, "nxt": "/problem/23_amc12A_p20", "prev": "/problem/23_amc12A_p18"}}