Logarithm

In mathematics, a logarithm is a function that gives the in the equation bn = x. It is usually written as logb x = n. For example:

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: !, 3^4 = 81 mbox{, thus } log_3 81 = 4

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The logarithm is one of three closely related functions. With bn = x, b can be determined with radicals, n with logarithms, and x with exponentials.

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The negative of a logarithm is written as n = −logb x; an example of its use is in chemistry, where it expresses the concentration of protons (pH).

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An antilogarithm is used to show the inverse of the logarithm. It is written antilogb(n) and means the same as bn.

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A double logarithm is the inverse function of the double-exponential function. A super-logarithm or hyper-logarithm is the inverse function of the super-exponential function. The super-logarithm of x grows even more slowly than the double logarithm for large x.

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A discrete logarithm is a related notion in the theory of finite groups. For some finite groups, it is believed that the discrete logarithm is very hard to calculate, whereas discrete exponentials are quite easy. This asymmetry has applications in cryptography.

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Function: In general (not in the mathematical but in the engineering sense), a function is a goal-oriented property of an entity. The carrier of a function is a process; therefore, is possible to realise the same function using different physical processes, and one process can be a carrier of multiple funct...

Radical: Radical is derived from the Latin word radix, which means "root". In various fields of endeavor, it can mean:...

Exponentials: REDIRECT Exponential function...