{"status": "success", "data": {"description_md": "Let $x$, $y$, and $z$ all exceed 1 and let $w$ be a positive number such that $$\\log_x w = 24,\\quad \\log_y w = 40 \\quad\\text{and}\\quad \\log_{xyz} w = 12. $$Find $\\log_z w$.\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</span>, <span class=\"katex--inline\">y</span>, and <span class=\"katex--inline\">z</span> all exceed 1 and let <span class=\"katex--inline\">w</span> be a positive number such that <span class=\"katex--display\">\\log_x w = 24,\\quad \\log_y w = 40 \\quad\\text{and}\\quad \\log_{xyz} w = 12.</span>Find <span class=\"katex--inline\">\\log_z w</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": "1983 AIME Problem 1", "can_next": true, "can_prev": false, "nxt": "/problem/83_aime_p02", "prev": ""}}