{"status": "success", "data": {"description_md": "Let $a > 1$ and $x > 1$ satisfy $\\log_a(\\log_a(\\log_a 2) + \\log_a 24 - 128) = 128$ and $\\log_a(\\log_a x) = 256$. Find the remainder when $x$ is divided by $1000$.\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\">a &gt; 1</span> and <span class=\"katex--inline\">x &gt; 1</span> satisfy <span class=\"katex--inline\">\\log_a(\\log_a(\\log_a 2) + \\log_a 24 - 128) = 128</span> and <span class=\"katex--inline\">\\log_a(\\log_a x) = 256</span>. Find the remainder when <span class=\"katex--inline\">x</span> is divided by <span class=\"katex--inline\">1000</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": 6, "problem_name": "2017 AIME I Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/17_aime_I_p15", "prev": "/problem/17_aime_I_p13"}}