Math natural logarithm

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Logarithms are useful, but there is a particular kind of logarithm
that is used the most often: the *natural* logarithm. This is just the
logarithm to the base [e]. In fact, the natural logarithm is so useful
that people often say "ln(n)" instead of log[e](n). math forum; Now, why is all
this important? It's hard to say without going into a lot of details,
but here's a little hint of the interesting things about e and ln(n):

Think about (1+1/n)^n for some value n. For n=1, this is 2. For n=2,
this is 2.25. For n=5, this is 2.48832. For n=10, this is 2.5937....
For n=100, this is 2.7048.... For n=10000, this is 2.7169.... Can you
guess what happens to (1+1/n)^n as n gets larger and larger? In fact,
it becomes e. A way of expressing this in mathematical notation is

lim (1+1/n)^n = e.
n->infinity

(the "lim" stands for "limit"; we say "the limit as n goes to infinity
of the quantity one plus one over n to the nth power is e.)

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