Infinite Powers: How Calculus Reveals the Secrets of the Universe

by Steven H. Strogatz

In other words, when we multiply two numbers together and then take their log, the result is the sum (not the product!) of their individual logs. In that sense, logarithms replace multiplication problems with addition problems, which are much easier. This is why logarithms were invented. They sped up calculations tremendously. Instead of having to deal with Herculean multiplication problems, square roots, cube roots, and the like, such calculations could be turned into addition problems and then solved with the help of a lookup table known as a table of logarithms. The idea of logarithms was in the air in the early seventeenth century, but much of the credit for popularizing them goes to the Scottish mathematician John Napier, who published his Description of the Wonderful Rule of Logarithms in 1614. A decade later, Johannes Kepler enthusiastically used the new calculational tool when he was compiling astronomical tables about the positions of the planets and other heavenly bodies. Logarithms were the supercomputers of their era.