{"status": "success", "data": {"description_md": "A circle has a radius of $\\log_{10}{(a^2)}$ and a circumference of $\\log_{10}{(b^4)}$. What is $\\log_{a}{b}$?\n\n$\\textbf{(A)}\\ \\frac{1}{4\\pi} \\qquad \\textbf{(B)}\\ \\frac{1}{\\pi} \\qquad \\textbf{(C)}\\ \\pi \\qquad \\textbf{(D)}\\ 2\\pi \\qquad \\textbf{(E)}\\ 10^{2\\pi}$<br>\n___\nFull 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>A circle has a radius of <span class=\"katex--inline\">\\log_{10}{(a^2)}</span> and a circumference of <span class=\"katex--inline\">\\log_{10}{(b^4)}</span>. What is <span class=\"katex--inline\">\\log_{a}{b}</span>?</p>&#10;<p><span class=\"katex--inline\">\\textbf{(A)}\\ \\frac{1}{4\\pi} \\qquad \\textbf{(B)}\\ \\frac{1}{\\pi} \\qquad \\textbf{(C)}\\ \\pi \\qquad \\textbf{(D)}\\ 2\\pi \\qquad \\textbf{(E)}\\ 10^{2\\pi}</span><br/></p>&#10;<hr/>&#10;<p>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": 3, "problem_name": "2008 AMC 12B Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/08_amc12B_p15", "prev": "/problem/08_amc12B_p13"}}