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Algebra Level 3

20112012×20132014 \large { \color{#D61F06}{2011} }^{ \color{teal}{2012} } \times { \color{#D61F06}{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

  • log102011=3.3034120705967 \log_{10} 2011 = 3.3034120705967 \ldots

  • log102013=3.3038437748886 \log_{10} 2013 = 3.3038437748886 \ldots

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