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431 Rh 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