{"status": "success", "data": {"description_md": "**POTD November 26, 2023**\n**Author:** qgek\n\nLet $xy^2 = 100$, with $1 \\le x \\le 10$. the smallest value of $(\\log x)^2$ + $(\\log$ $y)^2$ can be expressed as $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m + n$.", "description_html": "<p><strong>POTD November 26, 2023</strong><br/>&#10;<strong>Author:</strong> qgek</p>&#10;<p>Let <span class=\"katex--inline\">xy^2 = 100</span>, with <span class=\"katex--inline\">1 \\le x \\le 10</span>. the smallest value of <span class=\"katex--inline\">(\\log x)^2</span> + <span class=\"katex--inline\">(\\log</span> <span class=\"katex--inline\">y)^2</span> can be expressed as <span class=\"katex--inline\">\\frac{m}{n}</span>, where <span class=\"katex--inline\">m</span> and <span class=\"katex--inline\">n</span> are relatively prime positive integers. Find <span class=\"katex--inline\">m + n</span>.</p>&#10;", "hints_md": "AM-**Q**M", "hints_html": "<p>AM-<strong>Q</strong>M</p>&#10;", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "Problem of the Day #7", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}