Ive repeatedly asked people and my teachers how to solve logs by hand, and ive always got the same answer "They used tables and/or taylor series" but when i ask how the tables were made no one seems to know. So i am curious as to how John Napier and other mathematicians at the time found the values for their log tables. Was it just repeated trial and error? Is their some repeated algorithm? (other then those damn taylor series Hahaha) Also how would i calculate BY HAND: 10^k if we assume K is irrational and/or trancendental? thanks a ton!