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## Definitions

### General

The logarithm of a number x to a base n, is a power p so that n^{p}= x. In modern notation logarithm is written as . Any positive real number has a logarithm to a positive real base (except base 1). For any valid base, logarithm of 1 is 0, while the logarithm of 0 approaches negative infinity. Changing between bases can be done with the formula:

### Common bases

In practice, some logarithmic bases find more frequent use than others. Such common bases are 10 (decimal logarithm, or ), 2 (binary logarithm, ) and the mathematical constant e≈2.718, (natural logarithm, )

### Properties

The derivative of the logarithm function is:

The integral of the decimal logarithm function is given by:

Identities: