{"status": "success", "data": {"description_md": "Positive numbers $ x$, $ y$, and $ z$ satisfy $ xyz = 10^{81}$ and $ (\\log_{10}x)(\\log_{10} yz) + (\\log_{10}y) (\\log_{10}z) = 468$. Find $ \\sqrt {(\\log_{10}x)^2 + (\\log_{10}y)^2 + (\\log_{10}z)^2}$.\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>Positive numbers $ x$, $ y$, and $ z$ satisfy $ xyz = 10^{81}$ and $ (\\log_{10}x)(\\log_{10} yz) + (\\log_{10}y) (\\log_{10}z) = 468$. Find $ \\sqrt {(\\log_{10}x)^2 + (\\log_{10}y)^2 + (\\log_{10}z)^2}$.</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": "2010 AIME II Problem 5", "can_next": true, "can_prev": true, "nxt": "/problem/10_aime_II_p06", "prev": "/problem/10_aime_II_p04"}}