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Topic: Logarithm

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  Logarithm - Wikipedia, the free encyclopedia
Logarithms to various bases: red is to base e, green is to base 10, and purple is to base 1.7.
Therefore, logarithms are useful for making lengthy numerical operations easier to perform and, before the advent of electronic computers, they were widely used for this purpose in fields such as astronomy, engineering, navigation, and cartography.
The discrete logarithm is a related notion in the theory of finite groups.
en.wikipedia.org /wiki/Logarithm   (2698 words)

 Natural logarithm - Wikipedia, the free encyclopedia
The natural logarithm, formerly known as the hyperbolic logarithm, is the logarithm to the base e, where e is equal to 2.718281828459...
In other words, the logarithm function is a bijection from the set of positive real numbers to the set of all real numbers.
Logarithms can be defined to any positive base other than 1, not just e, and they are always useful for solving equations in which the unknown appears as the exponent of some other quantity.
en.wikipedia.org /wiki/Natural_logarithm   (997 words)

 Logarithm - LoveToKnow 1911
Logarithms were originally invented for the sake of abbreviating arithmetical calculations, as by their means the operations of multiplication and division may be replaced by those of addition and subtraction, and the operations of raising to powers and extraction of roots by those of multiplication and division.
The logarithm is also a function of frequent occurrence in analysis, being regarded as a known and recognized function like sin x or tan x; but in mathematical investigations the base generally employed is not 10, but a certain quantity usually denoted by the letter e, of value 2.71828 18284...
The logarithms are strictly Napierian, and the arrangement is identical with that in the canon of 1614.
www.1911encyclopedia.org /Logarithm   (9481 words)

 Online Encyclopedia and Dictionary - Logarithm
The logarithm functions are the inverses of the exponential functions.
Logarithms convert multiplication to addition, division to subtraction (making them isomorphisms between the field operations), exponentiation to multiplication, and roots to division (making logarithms crucial to slide rule construction).
Logarithms are useful in order to solve equations in which the unknown appears in the exponent, and they often occur as the solution of differential equations because of their simple derivatives.
www.fact-archive.com /encyclopedia/Logarithm   (1409 words)

 Encyclopedia :: encyclopedia : Logarithm   (Site not responding. Last check: 2007-10-22)
Logarithms determine n when given x; n is the number of times that x must be divided by b to reach 1.
One simply found the logarithms of both numbers (multiply and divide) or the first number (power or root, where one number is already an exponent) in a table of common logarithms, performed a simpler operation on those, and found the result on a table.
In abstract algebra, this property of the logarithm functions can be summarized by noting that any logarithm function with a fixed base is a group isomorphism from the group of strictly positive real numbers under multiplication to the group of all real numbers under addition.
www.hallencyclopedia.com /Logarithm   (2044 words)

 Learn more about Logarithm in the online encyclopedia.   (Site not responding. Last check: 2007-10-22)
In mathematics, the logarithm functions are the inverses of the exponential functions.
Binary logarithms are useful in determining characteristics of functions, such as the order of such functions that exhibit this behaviour.
Logarithms are also useful in order to solve equations in which the unknown appears in the exponent, and they often occur as the solution of differential equations because of their simple derivatives.
www.onlineencyclopedia.org /l/lo/logarithm.html   (654 words)

 PlanetMath: logarithm
By the very first identity, any logarithm restricted to the set of positive integers is an additive function.
Before the advent of electronic calculators and computers, tables of logarithms and the logarithmic slide rule were essential computational aids.
This is version 16 of logarithm, born on 2002-02-21, modified 2006-07-27.
planetmath.org /encyclopedia/Logarithm.html   (277 words)

 Logarithms   (Site not responding. Last check: 2007-10-22)
Logarithms may be manipulated with the combination rules.
The logarithm to the base b of the variable x is defined as the power to which you would raise b to get x.
If the logarithm to the base b of x is equal to y, then b raised to the y power will give you the value x.
hyperphysics.phy-astr.gsu.edu /hbase/logm.html   (187 words)

 KryssTal : A Look At Logarithms
Logarithms turned out to be one of the most important aids to computation before the arrival of computers and calculators.
Remember, logarithms are really indices so the laws are similar to the laws of indices.
Logarithms can be used to solve algebraic equations where the unknown is in the index.
www.krysstal.com /logarithms.html   (1248 words)

The logarithm, therefore, of any sine is a number very neerely expressing the line which increased equally in the meene time whiles the line of the whole sine decreased proportionally into that sine, both motions being equal timed and the beginning equally shift.
The logarithm of the number 70 is 1.84510, and the logarithm of the number 700 is 2.84510.
Logarithms had reached their full potential and most of what was done after 1694 was calculating logarithms to different bases.
www.thocp.net /reference/sciences/mathematics/logarithm_hist.htm   (1934 words)

 Logarithm Tutorial   (Site not responding. Last check: 2007-10-22)
The logarithm is a mathematical function much the same as more familiar functions such as the square root, sin, or absolute value functions.
One important difference between the logarithm function and most other mathematical functions is that there are different varieties or flavors of the logarithm function.
First, the scale of the logarithmic axis represents the log of a variable; however, the axis is labeled using the values of the original variable.
aghort.nmsu.edu /soils/soil_physics/tutorials/log/log_home.html   (1906 words)

This is just an identity arising from the definition of the logarithm, but it is sometimes useful in manipulating formulas.
The integer part is called the characteristic of the logarithm, and the fractional part is called the mantissa.
Logarithms were used in the days before computers to perform multiplication of large numbers.
ccrma-www.stanford.edu /~jos/mdft/Logarithms.html   (359 words)

 Highbeam Encyclopedia - Search Results for logarithm   (Site not responding. Last check: 2007-10-22)
logarithm LOGARITHM [logarithm] [Grrelation number], number associated with a positive number, being the power to which a third number, called the base, must be raised in order to obtain the given positive number.
For example, the logarithm of 100 to the base 10 is 2, written log 10 100=2, since 10 2 =100.
He invented logarithms and wrote Mirifici logarithmorum canonis descriptio (1614), containing the first logarithmic table and the first use of the word logarithm.
www.encyclopedia.com /articles/07581.html   (595 words)

 Logarithms - Topics in precalculus
In any base, the logarithm of the base itself is 1.
Logarithms replace a geometric series with an arithmetic series.
"The logarithm of a quotient is equal to the logarithm of the numerator
www.themathpage.com /aPreCalc/logarithms.htm   (699 words)

 Logarithm Sp 99   (Site not responding. Last check: 2007-10-22)
Logarithm is the exponent to which a number is raised to produce a given number.
The common logarithm, commonly abbreviated as log, refers to the exponent to which 10 has to be raised, and the natural logarithm, abbreviated ln, refers to the exponent to which e has to be raised.
Logarithm of more complex numbers require the use of a calculator or a log table.
www.towson.edu /~yau/LogarithmSp99.htm   (1716 words)

 Logarithmic and exponential functions - Topics in precalculus
The solution may be expressed as a logarithm.
Use the laws of logarithms (Topic 20) to write the following as one logarithm.
If two logarithms with the same base are equal, then their arguments are equal.
www.themathpage.com /aPreCalc/logarithmic-exponential-functions.htm   (634 words)

 exponential function   (Site not responding. Last check: 2007-10-22)
The inverse of the exponential function is the logarithmic function or logarithm.
For 2 as the base of the logarithm the binary logarithm lb(x) is the case.
In the time of the logarithmic tables the cologarithm was used to prevent negative results.
www.2dcurves.com /exponential/exponentiale.html   (869 words)

 What is logarithm? - a definition from Whatis.com - see also: logarithmic
A logarithm is an exponent used in mathematical calculations to depict the perceived levels of variable quantities such as visible light energy, electromagnetic field strength, and sound intensity.
When the base-10 logarithm of a quantity increases by 1, the quantity itself increases by a factor of 10.
In theoretical science and mathematics, another logarithmic base is encountered: the transcendental number e, which is approximately equal to 2.71828.
whatis.techtarget.com /definition/0,,sid9_gci213698,00.html   (259 words)

The logarithm is perhaps the single, most useful arithmetic concept in all the sciences; and an understanding of them is essential to an understanding of many scientific ideas.
Logarithms may be defined and introduced in several different ways.
Radioactivity behaves in such a way that the number N of radioactive atoms remaining at a later time t is given by a linear variation of the logarithm of N with t.
www.physics.uoguelph.ca /tutorials/LOG   (1198 words)

 Hard Cock
The sum of lines stabilizes the natural logarithm, as was to be shown.
The integral on a surface, excepting an obvious case, essentially counterbalances the decreasing natural logarithm that will undoubtedly lead us to to true hard cock The criterion stabilizes a maximum, obviously showing all bosh of the aforesaid.
It is necessary to note, that integral develops the natural logarithm, thus, instead of 13 it is possible to take any other constant.
site.neogen.ro /hardcock/images/img_983055.html   (779 words)

 PlanetMath: discrete logarithm
It is a difficult problem to compute the discrete logarithm, while powering is very easy.
Cross-references: cryptography, properties, satisfies, basis, logarithm, primitive root, cyclic, group, prime
This is version 3 of discrete logarithm, born on 2004-12-21, modified 2004-12-25.
planetmath.org /encyclopedia/DiscreteLogarithm.html   (72 words)

 Derivative of the Natural Logarithm
Basic properties of the natural logarithm are derived from properties of the exponential function and general facts about inverse functions.
The domain of the natural logarithm is the set of all positive real numbers.
We can compute the derivative of the natural logarithm by using the general formula for the derivative of an inverse function.
oregonstate.edu /instruct/mth251/cq/Stage6/Lesson/log.html   (274 words)

 Complex logarithm
The complex natural logarithm is the inverse exponential function.
Here we show the principal part of the logarithm, which is defined by restricting the argument arg(z) to the interval [-Pi, Pi].
The complex logarithm has a singularity at z=0 (here the function value is infinite) and a zero at z=1.
www.kfunigraz.ac.at /imawww/vqm/pages/complex/15_log.html   (125 words)

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