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:

Related Topics:
Mathematics - Function

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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.

Related Topics:
Radical - 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).

Related Topics:
Concentration - Proton - 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.

Related Topics:
Double-exponential function - Super-exponential function

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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.

Related Topics:
Discrete logarithm - Groups - Finite group - Cryptography

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