{"status": "success", "data": {"description_md": "The numbers $\\log(a^3b^7)$, $\\log(a^5b^{12})$, and $\\log(a^8b^{15})$ are the first three terms of an arithmetic sequence, and the $12^\\text{th}$ term of the sequence is $\\log(b^n)$. What is $n$?\n\n$\\mathrm{(A)}\\ 40\\qquad\\mathrm{(B)}\\ 56\\qquad\\mathrm{(C)}\\ 76\\qquad\\mathrm{(D)}\\ 112\\qquad\\mathrm{(E)}\\ 143$\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>The numbers  <span class=\"katex--inline\">\\log(a^3b^7)</span> ,  <span class=\"katex--inline\">\\log(a^5b^{12})</span> , and  <span class=\"katex--inline\">\\log(a^8b^{15})</span>  are the first three terms of an arithmetic sequence, and the  <span class=\"katex--inline\">12^\\text{th}</span>  term of the sequence is  <span class=\"katex--inline\">\\log(b^n)</span> . What is  <span class=\"katex--inline\">n</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\mathrm{(A)}\\ 40\\qquad\\mathrm{(B)}\\ 56\\qquad\\mathrm{(C)}\\ 76\\qquad\\mathrm{(D)}\\ 112\\qquad\\mathrm{(E)}\\ 143</span> </p>&#10;<hr><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>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2008 AMC 12A Problem 16", "can_next": true, "can_prev": true, "nxt": "/problem/08_amc12A_p17", "prev": "/problem/08_amc12A_p15"}}