History of Logarithm

	Revision 19 . . November 13, 2001 11:44 am by AxelBoldt
	Revision 18 . . November 13, 2001 8:20 am by AxelBoldt
	Revision 17 . . (edit) August 25, 2001 3:06 am by (logged).176.164.xxx [*fixed formatting.]

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Difference (from prior major revision) (author diff)

Changed: 1,9c1

In mathematics, the logarithm function is the inverse of the exponential function. For instance, if y is x to the power p, we also say that p is the logarithm of y in the base x (meaning p is the power we have to raise x to, to get y.) Logarithms were invented by John Napier in the early 1600s. In mathematical notation, we can write: If : y = xp then : p = logxy.

In mathematics, the logarithm functions are the inverses of the exponential functions. If y is x to the power p, y = xp, we also say that p is the logarithm of y in the base x (meaning p is the power we have to raise x to, in order to get y), and we write p = logxy. For instance, log10100 = 2 and log28 = 3. See /Identities? for several rules governing the logarithm functions.

Added: 10a3

Logarithms were invented by John Napier in the early 1600s. Before the widespread availability of electronic computers, logarithms were widely used as a calculating aid, both with [tables of logarithms]? and slide rules. The basic idea here is that the logarithm of a product is the sum of the logarithms, and adding is much easier than multiplication. Nowadays, the main use for logarithms is in solving equations in which the unknown(s) occur in the exponent.

Changed: 13,17c6

When dealing with the logarithms to the base e, it is common especially to denote loge by ln, especially if there is any likelihood that the reader might think that base 10 or base 2 logarithms might be meant. In most pure mathematical work, log is used to denote loge, in most engineering work, it means log10, while in information theory, it often means log2. Whenever a possibility for ambiguity exists, this ambiguity should be resolved by explicitly writing what you mean. Before the widespread availability of electronic computers, logarithms were widely used as a calculating aid. This was seen in publications of [tables of logarithms]? and also in the slide rule. The basic idea here is that the logarithm of a product is the sum of the logarithms, and adding is much easier than multiplication.

When dealing with the logarithms to the base e, it is common especially to denote loge by ln, especially if there is any likelihood that the reader might think that base 10 or base 2 logarithms might be meant. In most pure mathematical work, log is used to denote loge, in most engineering work, it means log10, while in information theory, it often means log2. Whenever a possibility for ambiguity exists, this ambiguity should be resolved by explicitly writing out the base.

Changed: 21c10

The logarithms of imaginary numbers are closely connected with the normal trigonometric functions (See Trigonometry). This can be seen by starting with Euler's formula:

The logarithms of imaginary numbers are closely connected with the trigonometric functions (see trigonometry). This can be seen by starting with Euler's formula:

Changed: 42,43c31

/Identities?