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 (18031882)
“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 (18971962)
“Be near me when I fade away,
To point the term of human strife,
And on the low dark verge of life
The twilight of eternal day.”
—Alfred Tennyson (18091892)