{"status": "success", "data": {"description_md": "In the equation $\\cos(x^2) = \\log_{b} x$, for some positive integer $b$, we are given that there are at least $2024$ real solutions. What is the minimum value of $b$?\n    \n$\\textbf{(A)}~80\\qquad\\textbf{(B)}~81\\qquad\\textbf{(C)}~82\\qquad\\textbf{(D)}~83\\qquad\\textbf{(E)}~84$", "description_html": "<p>In the equation <span class=\"katex--inline\">\\cos(x^2) = \\log_{b} x</span>, for some positive integer <span class=\"katex--inline\">b</span>, we are given that there are at least <span class=\"katex--inline\">2024</span> real solutions. What is the minimum value of <span class=\"katex--inline\">b</span>?</p>&#10;<p><span class=\"katex--inline\">\\textbf{(A)}~80\\qquad\\textbf{(B)}~81\\qquad\\textbf{(C)}~82\\qquad\\textbf{(D)}~83\\qquad\\textbf{(E)}~84</span></p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "2024 Mock AMC 12 - Problem 17", "can_next": true, "can_prev": true, "nxt": "/problem/2024_mock_amc12-p18", "prev": "/problem/2024_mock_amc12-p16"}}