Logarithms: An Introduction

It was a Baron of the Scottish aristocracy, Lord John Napier (1550-1617), who invented these unusual numbers (his work on them was officially published three years before his death). At first, he had called them "artificial numbers". It was only later that he chose to rename them "logarithms" meaning numbers that indicate ratios because the difference of two logarithms determines the ratio of the two numbers they represent. As is often the case with new discoveries or inventions, acceptance of these artificial numbers was lukewarm and there was considerable resistance to adopt them by those in the scientific community of the time, with the notable exception of Johannes Kepler, a German mathematician and astronomer.

From these beginnings, it is now known that various unit measurements in scientific or science-related disciplines are expressed as logarithms of other quantities. For example, the pH factor in chemistry, the apparent magnitude of the stars from our earthly perspective, the decibel in telecommunications and engineering, the Richter scale magnitude of earthquakes, a way of measuring distance in the hyperbolic geometry of the Poincaré half plane, and semitones in music are all defined using logarithms to various bases.

Last Updated by SAS October 07, 2026, 16:00:49