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 the, origin and/or term:
“The essence of morality is a questioning about morality; and the decisive move of human life is to use ceaselessly all light to look for the origin of the opposition between good and evil.”
—Georges Bataille (1897–1962)
“High treason, when it is resistance to tyranny here below, has its origin in, and is first committed by, the power that makes and forever re-creates man.”
—Henry David Thoreau (1817–1862)
“Here the term ‘language-game’ is meant to bring into prominence the fact that the speaking of language is part of an activity, of a form of life.”
—Ludwig Wittgenstein (1889–1951)