Logarithm (13466 bytes)
1: ...is found using an [[exponential function]]. A '''logarithm''' is a [[function (mathematics)|function]] used ...
3: ...tion|inverses]] of the [[exponential function]]s. Logarithms convert multiplication to addition, division to ...
5: ...tilogarithm''' is used to show the inverse of the logarithm. It is written antilog(''n'') and means the same...
7: ...arithm of ''x'' grows even slower than the double logarithm for large ''x''.
9: ...e finite groups, it is believed that the discrete logarithm is very hard to calculate, whereas discrete expon...

Common logarithm (3392 bytes)
1: [[Image:Graph of common logarithm.png|thumb|450px|right|]]
2: The '''common logarithm''' is the [[logarithm]] with base 10.
4: ... In addition, [[slide rule]]s worked by using a [[logarithmic scale]].
6: ...ers not between 1 and 10, since if one wanted the logarithm of, for example, 120, one would know that
10: ...20, called the '''characteristic''' of the common logarithm of 120, is 2.

Discrete logarithm (2336 bytes)
1: ...hematics)|group theory]] in analogy to ordinary [[logarithm]]s.
7: ...n is a [[group isomorphism]], called the discrete logarithm to base ''b''.
9: The familiar base change formula for ordinary logarithms remains valid: if ''c'' is another generator of ...
14: For some groups, computing discrete logarithms is believed to be difficult, while the inverse p...
17: Newer cryptography applications use discrete logarithms in cyclic subgroups of [[elliptic curve]]s over ...

Binary logarithm (2741 bytes)
1: [[Image:Binary logarithm plot.png|thumbnail|right|200px|Plot of log<sub>2<...
3: ...hm]] in the base 2 (log₂''n''). Binary logarithm is frequently written lg ''n''. It is the [[inver...
5: Binary logarithm is often used in [[computer science]] and [[infor...
8: ...ion]] and [[information entropy]] involves binary logarithm; this is needed because the [[unit]] of informati...
10: Binary logarithm also frequently appears in the [[analysis of algo...

Iterated logarithm (1813 bytes)
1: ...og^*''n'', is the number of times the [[logarithm]] function must be iteratively applied before th...
10: [[Image:Iterated_logarithm.png|right|300px|thumb|'''Figure 1.''' Demonstrati...
11: ... needed in Figure 1 to reach the y-axis above the logarithm function.
13: The iterated logarithm is useful in [[analysis of algorithms]] and their...
17: ...ction]]. For all practical purposes, the iterated logarithm may be considered to be a constant.

Natural logarithm (8598 bytes)
1: ...pier]], it is sometimes known as the '''Napierian logarithm'''.
3: [[image:ln .png|The natural logarithm goes to minus infinity as x goes to 0.]]<br/>
9: ...og_e(''x'')" when they mean the natural logarithm of ''x'', and take "log(''x'')" to mean log<sub>1...
11: ... and use only "ln(''x'')" to refer to the natural logarithm of ''x''. As recently as 1984, [[Paul Halmos]] i...
13: ...''x'' and log₁₀(''x'') for the base-10 logarithm of ''x''.

List of logarithm topics (1521 bytes)
1: This is a '''list of [[logarithm]] topics''', by Wikipedia page. See also the [[li...
4: *[[antilogarithm]]
8: *[[Binary logarithm]]
11: *[[Common logarithm]]
12: *[[Discrete logarithm]]

Law of the iterated logarithm (1549 bytes)
2: the '''law of the iterated logarithm''' is the name given to several theorems which de...
3: ...ginal statement (1924) of the law of the iterated logarithm is due to [[Aleksandr Yakovlevich Khinchin|A. Ya....
6: ...e of the simpler forms of the law of the iterated logarithm can be stated as follows (Theorem 3.52 in Breiman...
21: * A. Kolmogoroff. "Über das Gesetz des iterierten Logarithmus". ''Mathematische Annalen'', 101:126-135, 1929....

LG (629 bytes)
3: * [[logarithm|lg]] - an abbreviation for logarithm of the base 2in [[informatics]] (an alternative t...

Parabolic fractal distribution (722 bytes)
1: ...a population is a [[quadratic polynomial]] of the logarithm of the rank. This can markedly improve the fit ov...

Geometric standard deviation (2686 bytes)
9: then taking the [[natural logarithm]] of both sides results in
11: The logarithm of a product is a sum of logarithms, so
29: ...ibution is a distribution which is normal for the logarithm
30: transformed values. By a simple set of logarithm transformations we see that the
42: ...ic mean]], [[log-normal distribution]], [[natural logarithm]]

Transcendental function (998 bytes)
3: The [[logarithm]] and the [[exponential function]] are examples o...
7: ... of transcendental functions, in the way that the logarithm function arises from the reciprocal function. In ...

Joost Buerghi (126 bytes)
1: ...zerland|Swiss]] mathematician who developed the [[logarithm]] table in [[1588]].

Entropy (ecology) (1766 bytes)
20: ...]]. The [[thermodynamic]] entropy uses [[natural logarithm]] (base <math>e</math>), so that the constant <ma...

Partial function (1064 bytes)
7: ...al number]]s to the reals is only partial, as the logarithm of non-positive reals is not a real number.

Significand (2125 bytes)
12: ... [[Latin]] word for ''makeweight''); see [[common logarithm]] for more on this older meaning.
14: ...in that the fractional part of a logarithm is the logarithm of the significand for the same base, plus a cons...

Sound power (1026 bytes)
15: ...ce sound power. It is thus a [[logarithmic scale|logarithmic measure]].

Principal value (3295 bytes)
6: Consider the complex logarithm function log ''z''. It is defined as the complex ...
28: We have examined the logarithm function above, ie.,
30: ...e clear that we obtain the principal value of the logarithm, and we write
33: So far we have only considered the logarithm function. What about exponents? Consider ''z''<su...

Euler's constant (173 bytes)
3: ...athematical constant)|e]]'' the base of natural [[logarithm]]s

Taylor rule (865 bytes)
6: ...c Product|GDP]], and <math>\bar y_t</math> is the logarithm of potential output, as determined by a linear tr...

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