In the context of linear regression in the social sciences, Gelman and Hill write:
We prefer natural logs (that is, logarithms base e e) because, as described above, coefficients on the natural-log scale are directly interpretable as approximate proportional differences: with a coefficient of 0.06, a difference of 1 in x corresponds to an approximate 6% difference in y, and so forth.
 Andrew Gelman and Jennifer Hill (2007). Data Analysis using Regression and Multilevel/Hierarchical Models. Cambridge University Press: Cambridge; New York, pp. 60-61.