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2013 AMC 12A Question 21

AMC12 · 2013 AMC 12A

Question 21

Consider $$
\begin{gathered} A = \\ \tiny \log(2013 + \log(2012 + \log(2011 + \log(\cdots + \log(3 + \log 2)\cdots)))). \end{gathered}
$$

Which of the following intervals contains $A?$
  1. $(\log 2016, \log 2017)$
  2. $(\log 2017, \log 2018)$
  3. $(\log 2018, \log 2019)$
  4. $(\log 2019, \log 2020)$
  5. $(\log 2020, \log 2021)$