Origin of The Term natural Logarithm
Initially, it might seem that since the common numbering system is base 10, this base would be more "natural" than base e. But mathematically, the number 10 is not particularly significant. Its use culturally—as the basis for many societies’ numbering systems—likely arises from humans’ typical number of fingers. Other cultures have based their counting systems on such choices as 5, 8, 12, 20, and 60.
loge is a "natural" log because it automatically springs from, and appears so often in, mathematics. For example, consider the problem of differentiating a logarithmic function:
If the base b equals e, then the derivative is simply 1/x, and at x = 1 this derivative equals 1. Another sense in which the base-e-logarithm is the most natural is that it can be defined quite easily in terms of a simple integral or Taylor series and this is not true of other logarithms.
Further senses of this naturalness make no use of calculus. As an example, there are a number of simple series involving the natural logarithm. Pietro Mengoli and Nicholas Mercator called it logarithmus naturalis a few decades before Newton and Leibniz developed calculus.
Read more about this topic: Natural Logarithm
Famous quotes containing the words origin of, origin and/or term:
“For, though the origin of most of our words is forgotten, each word was at first a stroke of genius, and obtained currency, because for the moment it symbolized the world to the first speaker and to the hearer. The etymologist finds the deadest word to have been once a brilliant picture.”
—Ralph Waldo Emerson (1803–1882)
“Our theism is the purification of the human mind. Man can paint, or make, or think nothing but man. He believes that the great material elements had their origin from his thought.”
—Ralph Waldo Emerson (1803–1882)
“Most literature on the culture of adolescence focuses on peer pressure as a negative force. Warnings about the “wrong crowd” read like tornado alerts in parent manuals. . . . It is a relative term that means different things in different places. In Fort Wayne, for example, the wrong crowd meant hanging out with liberal Democrats. In Connecticut, it meant kids who weren’t planning to get a Ph.D. from Yale.”
—Mary Kay Blakely (20th century)