{"status": "success", "data": {"description_md": "If $x, y,$ and $z$ are positive integers that satisfy\n\n$$3^z + \\log_3(16x+17) = y $$\n\n$$\\log_{27}(128) - y\\log_{27}(2) = \\log_3(\\sqrt[3]{8x-5}) - 3^{z-1} $$\n\nFind the sum of all possible values of $x+y+z$.", "description_html": "<p>If <span class=\"katex--inline\">x, y,</span> and <span class=\"katex--inline\">z</span> are positive integers that satisfy</p>&#10;<p><span class=\"katex--display\">3^z + \\log_3(16x+17) = y</span></p>&#10;<p><span class=\"katex--display\">\\log_{27}(128) - y\\log_{27}(2) = \\log_3(\\sqrt[3]{8x-5}) - 3^{z-1}</span></p>&#10;<p>Find the sum of all possible values of <span class=\"katex--inline\">x+y+z</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "TxO Math Bowl 2024 - Individuals B - Problem 12", "can_next": true, "can_prev": true, "nxt": "/problem/txo2024indivsB-p13", "prev": "/problem/txo2024indivsB-p11"}}