Logarithms and Taylor Series

Question

Before Log Tables, how were they able to compute expressions such as $2^{2.221}$? I understand they could take a Taylor expansion of $\frac{1}{x}$, but how were they able to condense the expansion into what we know today as natural logarithms?

Answer 1

In fact, until log tables were available, there was no practical way to compute $a^b$ for any $b$ other than an integer or perhaps a half-integer.

A really excellent light reading book on such things is "e - the story of a number".

Answer 2

I am not even sure that people thought about elevation to a rational power before logarithms were developed.