{"status": "success", "data": {"description_md": "If $a\\geq b > 1,$ what is the largest possible value of $\\log_{a}(a/b) + \\log_{b}(b/a)?$\n\n$\\mathrm{(A)}\\ -2      \\qquad<br>\\mathrm{(B)}\\ 0     \\qquad<br>\\mathrm{(C)}\\ 2      \\qquad<br>\\mathrm{(D)}\\ 3      \\qquad<br>\\mathrm{(E)}\\ 4$\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>If  <span class=\"katex--inline\">a\\geq b &gt; 1,</span>  what is the largest possible value of  <span class=\"katex--inline\">\\log_{a}(a/b) + \\log_{b}(b/a)?</span> </p>&#10;<p> <span class=\"katex--inline\">\\mathrm{(A)}\\ -2      \\qquad\\mathrm{(B)}\\ 0     \\qquad\\mathrm{(C)}\\ 2      \\qquad\\mathrm{(D)}\\ 3      \\qquad\\mathrm{(E)}\\ 4</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": 5, "problem_name": "2003 AMC 12A Problem 24", "can_next": true, "can_prev": true, "nxt": "/problem/03_amc12A_p25", "prev": "/problem/03_amc12A_p23"}}