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2004 AMC 12A Question 16

AMC12 · 2004 AMC 12A

Question 16

The set of all real numbers $x$ for which $$
\small \log_{2004}(\log_{2003}(\log_{2002}(\log_{2001} x)))
$$ is defined is $\{x \mid x \gt c\}.$ What is the value of $c?$
  1. $0$
  2. $2001^{2002}$
  3. $2002^{2003}$
  4. $2003^{2004}$
  5. $2001^{2002^{2003}}$