{"status": "success", "data": {"description_md": "The set of all real numbers $x$ for which\n\n$$\\log_{2004}(\\log_{2003}(\\log_{2002}(\\log_{2001}{x})))$$<br>is defined is $\\{x\\mid x > c\\}$. What is the value of $c$?\n\n$\\textbf {(A) } 0\\qquad \\textbf {(B) }2001^{2002} \\qquad \\textbf {(C) }2002^{2003} \\qquad \\textbf {(D) }2003^{2004} \\qquad \\textbf {(E) }2001^{2002^{2003}}$\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 set of all real numbers  <span class=\"katex--inline\">x</span>  for which</p>&#10;<p> <span class=\"katex--display\">\\log_{2004}(\\log_{2003}(\\log_{2002}(\\log_{2001}{x})))</span> <br/>is defined is  <span class=\"katex--inline\">\\{x\\mid x &gt; c\\}</span> . What is the value of  <span class=\"katex--inline\">c</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf {(A) } 0\\qquad \\textbf {(B) }2001^{2002} \\qquad \\textbf {(C) }2002^{2003} \\qquad \\textbf {(D) }2003^{2004} \\qquad \\textbf {(E) }2001^{2002^{2003}}</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": "2004 AMC 12A Problem 16", "can_next": true, "can_prev": true, "nxt": "/problem/04_amc12A_p17", "prev": "/problem/04_amc12A_p15"}}