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Algebra Level 3

\[ \large { \color{red}{2011} }^{ \color{teal}{2012} } \times { \color{red}{2013}}^{ \color{teal}{2014} }\]

Find the number of digits of the number above when stated in decimal representation.

Details and Assumptions

You may use the following approximations

  • \( \log_{10} 2011 = 3.3034120705967 \ldots \)

  • \( \log_{10} 2013 = 3.3038437748886 \ldots \)

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