{"status": "success", "data": {"description_md": "Let $x,y$ and $z$ be real numbers satisfying the system \\begin{align*}<br>\\log_2(xyz-3+\\log_5 x) &= 5 \\\\<br>\\log_3(xyz-3+\\log_5 y) &= 4 \\\\<br>\\log_4(xyz-3+\\log_5 z) &= 4.<br>\\end{align*}Find the value of $|\\log_5 x|+|\\log_5 y|+|\\log_5 z|$.\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>Let <span class=\"katex--inline\">x,y</span> and <span class=\"katex--inline\">z</span> be real numbers satisfying the system \\begin{align*}<br/>\\log_2(xyz-3+\\log_5 x) &amp;= 5 \\<br/>\\log_3(xyz-3+\\log_5 y) &amp;= 4 \\<br/>\\log_4(xyz-3+\\log_5 z) &amp;= 4.<br/>\\end{align*}Find the value of <span class=\"katex--inline\">|\\log_5 x|+|\\log_5 y|+|\\log_5 z|</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": "2016 AIME II Problem 3", "can_next": true, "can_prev": true, "nxt": "/problem/16_aime_II_p04", "prev": "/problem/16_aime_II_p02"}}