  We show how Benford's Law (BL) for first, second, ..., digits, emerges from
the distribution of digits of numbers of the type $a^{R}$, with $a$ any real
positive number and $R$ a set of real numbers uniformly distributed in an
interval $[ P\log_a 10, (P +1) \log_a 10) $ for any integer $P$. The result is
shown to be number base and scale invariant. A rule based on the mantissas of
the logarithms allows for a determination of whether a set of numbers obeys BL
or not. We show that BL applies to numbers obtained from the {\it
multiplication} or {\it division} of numbers drawn from any distribution. We
also argue that (most of) the real-life sets that obey BL are because they are
obtained from such basic arithmetic operations. We exhibit that all these
arguments were discussed in the original paper by Simon Newcomb in 1881, where
he presented Benford's Law.
