The method of logarithms was publicly propounded by John Napier in 1614, in a book titled "Mirifici Logarithmorum Canonis Descriptio" ("Description of the Wonderful Rule of Logarithms").

Johannes Kepler, who used logarithm tables extensively to compile his "Ephemeris" and therefore dedicated it to Napier, remarked:By repeated subtractions Napier calculated for "L" ranging from 1 to 100. The result for "L"=100 is approximately 0.99999 = 1 − 10. Napier then calculated the products of these numbers with for "L" from 1 to 50, and did similarly with and . These computations, which occupied 20 years, allowed him to give, for any number "N" from 5 to 10 million, the number "L" that solves the equation

Napier first called "L" an "artificial number", but later introduced the word ""logarithm"" to mean a number that indicates a ratio: ("logos") meaning proportion, and ("arithmos") meaning number. In modern notation, the relation to natural logarithms is:

where the very close approximation corresponds to the observation that

The invention was quickly and widely met with acclaim. The works of Bonaventura Cavalieri (Italy), Edmund Wingate (France), Xue Fengzuo (China), and Johannes Kepler's "Chilias logarithmorum" (Germany) helped spread the concept further.

Napier
Bürgi
অয়লার
Modern form