{"status": "success", "data": {"description_md": "Real numbers $x$ and $y$ with $x,y>1$ satisfy $\\log_x(y^x)=\\log_y(x^{4y})=10.$ What is the value of $xy$?\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full 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>Real numbers <span class=\"katex--inline\">x</span> and <span class=\"katex--inline\">y</span> with <span class=\"katex--inline\">x,y&gt;1</span> satisfy <span class=\"katex--inline\">\\log_x(y^x)=\\log_y(x^{4y})=10.</span> What is the value of <span class=\"katex--inline\">xy</span>?</p>&#10;<hr><p>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code>. 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": "2024 AIME I Problem 2", "can_next": true, "can_prev": true, "nxt": "/problem/24_aime_I_p03", "prev": "/problem/24_aime_I_p01"}}