{"status": "success", "data": {"description_md": "How many distinct four-tuples $(a, b, c, d)$ of rational numbers are there with\n\n$a \\cdot \\log_{10} 2+b \\cdot \\log_{10} 3 +c \\cdot \\log_{10} 5 + d \\cdot \\log_{10} 7 = 2005$?\n\n$\\mathrm{(A)}\\ 0      \\qquad<br>\\mathrm{(B)}\\ 1      \\qquad<br>\\mathrm{(C)}\\ 17     \\qquad<br>\\mathrm{(D)}\\ 2004   \\qquad<br>\\mathrm{(E)}\\ \\text{infinitely many}$\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>How many distinct four-tuples  <span class=\"katex--inline\">(a, b, c, d)</span>  of rational numbers are there with</p>&#10;<p> <span class=\"katex--inline\">a \\cdot \\log_{10} 2+b \\cdot \\log_{10} 3 +c \\cdot \\log_{10} 5 + d \\cdot \\log_{10} 7 = 2005</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\mathrm{(A)}\\ 0      \\qquad\\mathrm{(B)}\\ 1      \\qquad\\mathrm{(C)}\\ 17     \\qquad\\mathrm{(D)}\\ 2004   \\qquad\\mathrm{(E)}\\ \\text{infinitely many}</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": "2005 AMC 12B Problem 17", "can_next": true, "can_prev": true, "nxt": "/problem/05_amc12B_p18", "prev": "/problem/05_amc12B_p16"}}