I have always wondered why men invented logarithms, and assumed it began as an intellectual curiosity. Perhaps it did, but I now know why it was readily adopted. Men who needed to perform complex calculations, such as merchants or logistics officers in the military, and of course the obvious people like scientists, often needed to multiply two numbers: say, then wanted to know the value of W in W = XY. With the invention of logarithms, all they needed to do was look it up in mathematical tables (remember, some of these people may be barely literate).
Tables were created showing the value of log(X) for every X. Then, noting log(W) = log(X) + log(Y), which was told to them, they could simply look up the values of log(X) and log(Y) in the table, add them together, and get a value of log(W). Then they looked in the same table to see what value of W corresponded to log(W), and they had their answer. Quick. Accurate. Convenient.
Of course, most of these people didn't know why this method worked, only that it did. These methods and tables were constructed around 1614 by John Napier, Joost Burgi, and Henry Briggs.
Source:
Will and Ariel Durant. The Age of Reason Begins. The Story of Civiliation. VII.
