Common vs natural

[AntonioLao]

There are two distinct types of logarithm widely found in mathematics: common and natural. The common one is base 10. The natural one is base e. The number e is the limit of an infinite series (see http://en.wikipedia.org/wiki/Natural_logarithm). It is an irrational number with non-repeating and non-terminating value of 2.718 281 182 459… The billion dollar question is why great mathematicians prefer natural log over common log? Gauss used it as a divisor to conjecture the prime numbers distribution. It is used in solving ordinary differential equations as integrating factors. It is used in quantum mechanics as the intractable phase factors. It is used in Maxwell’s theory of electromagnetism as sums or differences for defining hyperbolic sine and cosine. It is used in the exponential decays of radioactive materials. And it is used in the calculation of compound interests for financial loans and investments reaching their maturity values. But nobody bothers to ask, since everyone think that there is no question at all as long as it works!

[mkirkpatrick]

Give me the natural over common anyday!




regards michael.

[AntonioLao]

Mike,

What's your reason for wanting anything natural? The natural base of logarithm is also called hyperbolic would you still want then?