Page:Elementary algebra (1896).djvu/448

CHAPTER XLVI.

Exponential and Logarithmic Series.

536. The advantages of common logarithms have been explained in Art. 438, and in practice no other system is used. But in the first place these logarithms are calculated to another base and then transformed to base 10.

In the present chapter we shall prove certain formulæ, known as the Exponential and Logarithmic Series, and give a brief explanation of the way in which they are used in constructing a table of logarithms.

537. To expand $a^{x}$ in ascending powers of $x$.

By the Binomial Theorem, if $x>1$.

By putting $x=1$, we obtain

But ;