{"status": "success", "data": {"description_md": "Suppose that $a$, $b$, and $c$ are positive real numbers such that $a^{\\log_3 7} = 27$, $b^{\\log_7 11} = 49$, and $c^{\\log_{11} 25} = \\sqrt {11}$. Find<br>\n$$ a^{(\\log_3 7)^2} + b^{(\\log_7 11)^2} + c^{(\\log_{11} 25)^2}.\n$$\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>Suppose that <span class=\"katex--inline\">a</span>, <span class=\"katex--inline\">b</span>, and <span class=\"katex--inline\">c</span> are positive real numbers such that <span class=\"katex--inline\">a^{\\log_3 7} = 27</span>, <span class=\"katex--inline\">b^{\\log_7 11} = 49</span>, and <span class=\"katex--inline\">c^{\\log_{11} 25} = \\sqrt {11}</span>. Find<br/><br/>&#10;<span class=\"katex--display\"> a^{(\\log_3 7)^2} + b^{(\\log_7 11)^2} + c^{(\\log_{11} 25)^2}.&#10;</span></p>&#10;<hr/>&#10;<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>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2009 AIME II Problem 2", "can_next": true, "can_prev": true, "nxt": "/problem/09_aime_II_p03", "prev": "/problem/09_aime_II_p01"}}