{"status": "success", "data": {"description_md": "Suppose that $4^a = 5$, $5^b = 6$, $6^c = 7$, and $7^d = 8$. What is $a \\cdot b \\cdot c \\cdot d$?\n\n$\\mathrm{(A)} 1 \\qquad \\mathrm{(B)} \\frac{3}{2} \\qquad \\mathrm{(C)} 2 \\qquad \\mathrm{(D)} \\frac{5}{2} \\qquad \\mathrm{(E)} 3$", "description_html": "<p>Suppose that  <span class=\"katex--inline\">4^a = 5</span> ,  <span class=\"katex--inline\">5^b = 6</span> ,  <span class=\"katex--inline\">6^c = 7</span> , and  <span class=\"katex--inline\">7^d = 8</span> . What is  <span class=\"katex--inline\">a \\cdot b \\cdot c \\cdot d</span> ?</p>\n<p> <span class=\"katex--inline\">\\mathrm{(A)} 1 \\qquad \\mathrm{(B)} \\frac{3}{2} \\qquad \\mathrm{(C)} 2 \\qquad \\mathrm{(D)} \\frac{5}{2} \\qquad \\mathrm{(E)} 3</span> </p>\n<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 10B Problem 17", "can_next": true, "can_prev": true, "nxt": "/problem/05_amc10B_p18", "prev": "/problem/05_amc10B_p16"}}