Natural Logarithms
We defined the logarithmic function y = log_{a} x with base a. If a = 10, then y is called common logarithm of the number x. If a = e, we may define the logarithm of x to the base e as
Logarithms to the base e are called natural logarithms. It is customary to write log, x as log x. We recall that
log 1 = 0, log e = 1, e^{logx} = x and log (e)^{x} = x
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