{"status": "success", "data": {"description_md": "**POTD February 3, 2024**\n\nLet $A = (a, \\log_2 a), M = (m, \\log_2 m),$ and $B = (b, \\log_2 b)$ be three points on the graph of $y = \\log_2 x,$ where $0 < a < m < b.$ Let points $P$ and $Q$ be on segment $AB$ such that $MP$ is parallel to the y-axis and $MQ$ is parallel to the x-axis. Given that $AP=PQ=QB$, $\\frac{b}{a}$ can be expressed in the form $j+k \\sqrt l$, where $j,k$ and $l$ are positive integers and $l$ is not divisible by the square of any prime. Find $j+k+l$.", "description_html": "<p><strong>POTD February 3, 2024</strong></p>&#10;<p>Let <span class=\"katex--inline\">A = (a, \\log_2 a), M = (m, \\log_2 m),</span> and <span class=\"katex--inline\">B = (b, \\log_2 b)</span> be three points on the graph of <span class=\"katex--inline\">y = \\log_2 x,</span> where <span class=\"katex--inline\">0 &lt; a &lt; m &lt; b.</span> Let points <span class=\"katex--inline\">P</span> and <span class=\"katex--inline\">Q</span> be on segment <span class=\"katex--inline\">AB</span> such that <span class=\"katex--inline\">MP</span> is parallel to the y-axis and <span class=\"katex--inline\">MQ</span> is parallel to the x-axis. Given that <span class=\"katex--inline\">AP=PQ=QB</span>, <span class=\"katex--inline\">\\frac{b}{a}</span> can be expressed in the form <span class=\"katex--inline\">j+k \\sqrt l</span>, where <span class=\"katex--inline\">j,k</span> and <span class=\"katex--inline\">l</span> are positive integers and <span class=\"katex--inline\">l</span> is not divisible by the square of any prime. Find <span class=\"katex--inline\">j+k+l</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "Problem of the Day #60", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}