We write numbers in a base as a series of symbols (digits)
having each possible states (values). symbols, you have possible
combinations, so can be seen as the number of digits needed to
write The "log=size" equality is true within an error of 1
because the log is real-valued, whereas the number of digits is
an integer. For instance, Nonetheless, viewing the log merely as
the size can be helpful to get some intuition about it and gives
interesting insights in various fields where the log is central.
This may help beginners/students to get a better feel for the
log than from its usual mathematical definitions and properties
(e.g., inverse of exponentiation, integral of , tool to
transform multiplication into addition or to deal with large
numbers, etc.). It is a pity that this function has been
baptized with such a long and complicated name. Many students
would have an easier life were it named "size" instead of
"logarithm"! As an advanced example, in information theory, is
the number of different possible sta