{"status": "success", "data": {"description_md": "In a Martian civilization, all logarithms whose bases are not specified are assumed to be base $b$, for some fixed $b \\geq 2$. A Martian student writes down<br>\n$3 \\log(\\sqrt{x}\\log x) = 56$\n$\\log_{\\log (x)}(x) = 54$<br>\nand finds that this system of equations has a single real number solution $x > 1$. Find $b$.\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>In a Martian civilization, all logarithms whose bases are not specified are assumed to be base <span class=\"katex--inline\">b</span>, for some fixed <span class=\"katex--inline\">b \\geq 2</span>. A Martian student writes down<br/><br/>&#10;<span class=\"katex--inline\">3 \\log(\\sqrt{x}\\log x) = 56</span><br/>&#10;<span class=\"katex--inline\">\\log_{\\log (x)}(x) = 54</span><br/><br/>&#10;and finds that this system of equations has a single real number solution <span class=\"katex--inline\">x &gt; 1</span>. Find <span class=\"katex--inline\">b</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": 4, "problem_name": "2019 AIME II Problem 6", "can_next": true, "can_prev": true, "nxt": "/problem/19_aime_II_p07", "prev": "/problem/19_aime_II_p05"}}