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ALGEBRA
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hence the series (1) is the xth power of the series (2); that is,
and this is true however great n may be. If, therefore, n be
indefinitely increased, we have
The series
is usually denoted by e; hence
Write cx for x, then
Now let e^c=a, so that c=\log_a; by substituting for c
we obtain
This is the Exponential Theorem.
538. The series
which we have denoted by e, is very important, as it is the
base to which logarithms are first calculated. Logarithms
to this base are known as the Napierian system, so named
after Napier, the inventor of logarithms. They are also
