AMC 12A 2013 Problem 21

Consider

A=\log (2013+\log (2012+\log (2011+\log (\cdots+\log (3+\log 2) \cdots)))).

Which of the following intervals contains A ?

Answer Choices
A. (\log 2016, \log 2017)
B. (\log 2017, \log 2018)
C. (\log 2018, \log 2019)
D. (\log 2019, \log 2020)
E. (\log 2020, \log 2021)