logarithms - ορισμός. Τι είναι το logarithms
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Τι (ποιος) είναι logarithms - ορισμός

INVERSE OF THE EXPONENTIAL FUNCTION, WHICH MAPS PRODUCTS TO SUMS
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  • alt=An oval shape with the trajectories of two particles.
  • alt=A density plot. In the middle there is a black point, at the negative axis the hue jumps sharply and evolves smoothly otherwise.
  • alt=An illustration of the polar form: a point is described by an arrow or equivalently by its length and angle to the x-axis.
  • alt=A graph of the value of one mark over time. The line showing its value is increasing very quickly, even with logarithmic scale.
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  • alt=A graph of the logarithm function and a line touching it in one point.
  • alt=The graphs of two functions.
  • TI-83 Plus]] graphing calculator
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  • alt=A hyperbola with part of the area underneath shaded in grey.
  • alt=The hyperbola depicted twice. The area underneath is split into different parts.
  • alt=A photograph of a nautilus' shell.
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  • alt=Parts of a triangle are removed in an iterated way.
  • alt=An animation showing increasingly good approximations of the logarithm graph.

Logarithm         
The exponent of the power to which it is necessary to raise a fixed number to produce a given number. The fixed number is the base of the system. There are two systems; one, called the ordinary system, has 10 for its base, the other, called the Naperian system, has 2.71828 for its base. The latter are also termed hyperbolic logarithms, and are only used in special calculations.
logarithm         
['l?g?r??(?)m, -r??-]
¦ noun a quantity representing the power to which a fixed number (the base) must be raised to produce a given number.
Derivatives
logarithmic adjective
logarithmically adverb
Origin
C17: from mod. L. logarithmus, from Gk logos 'reckoning, ratio' + arithmos 'number'.
logarithm         
(logarithms)
In mathematics, the logarithm of a number is a number that it can be represented by in order to make a difficult multiplication or division sum simpler.
N-COUNT

Βικιπαίδεια

Logarithm

In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number x to the base b is the exponent to which b must be raised, to produce x. For example, since 1000 = 103, the logarithm base 10 of 1000 is 3, or log10 (1000) = 3. The logarithm of x to base b is denoted as logb (x), or without parentheses, logbx, or even without the explicit base, log x, when no confusion is possible, or when the base does not matter such as in big O notation.

The logarithm base 10 is called the decimal or common logarithm and is commonly used in science and engineering. The natural logarithm has the number e ≈ 2.718 as its base; its use is widespread in mathematics and physics, because of its very simple derivative. The binary logarithm uses base 2 and is frequently used in computer science.

Logarithms were introduced by John Napier in 1614 as a means of simplifying calculations. They were rapidly adopted by navigators, scientists, engineers, surveyors and others to perform high-accuracy computations more easily. Using logarithm tables, tedious multi-digit multiplication steps can be replaced by table look-ups and simpler addition. This is possible because the logarithm of a product is the sum of the logarithms of the factors:

log b ( x y ) = log b x + log b y , {\displaystyle \log _{b}(xy)=\log _{b}x+\log _{b}y,}

provided that b, x and y are all positive and b ≠ 1. The slide rule, also based on logarithms, allows quick calculations without tables, but at lower precision. The present-day notion of logarithms comes from Leonhard Euler, who connected them to the exponential function in the 18th century, and who also introduced the letter e as the base of natural logarithms.

Logarithmic scales reduce wide-ranging quantities to smaller scopes. For example, the decibel (dB) is a unit used to express ratio as logarithms, mostly for signal power and amplitude (of which sound pressure is a common example). In chemistry, pH is a logarithmic measure for the acidity of an aqueous solution. Logarithms are commonplace in scientific formulae, and in measurements of the complexity of algorithms and of geometric objects called fractals. They help to describe frequency ratios of musical intervals, appear in formulas counting prime numbers or approximating factorials, inform some models in psychophysics, and can aid in forensic accounting.

The concept of logarithm as the inverse of exponentiation extends to other mathematical structures as well. However, in general settings, the logarithm tends to be a multi-valued function. For example, the complex logarithm is the multi-valued inverse of the complex exponential function. Similarly, the discrete logarithm is the multi-valued inverse of the exponential function in finite groups; it has uses in public-key cryptography.

Παραδείγματα από το σώμα κειμένου για logarithms
1. Logarithms were invented by a mathematician called Al–Khwarizmi in the 7th century.
2. Lamb For two centuries they were the blue collar workers of science, mental laborers who could grind out logarithms as efficiently as other factory workers turned out pins.
3. "The more we discover how the human brain achieves intelligence the more we‘ll be able to use the same computational architecture and logarithms in computers," said Bostrom.
4. If so, I would like to propose a supplemental bill called the Parent Homework Relief Act, which would fund a corps of math experts who would make home visits at any time of day or night to help people like me wrestle through the nuances of logarithms, histograms, box plots, and all the other mind–blowing topics that encompass an 11th–grade algebra survey.
5. All they would see is the equivalent of logarithms in literature." Replying to Wood she concluded "it‘s all laughter in the dark – the title of a Nabokov novel and still the best term for the kind of writing I aspire to÷ not a division of head and heart, but the useful employment of both." White Teeth takes Archie, 47, middle–aged, washed–up, just returned from the brink of suicide; Clara, 1', Jamaican ex–Jehovah‘s Witness; their daughter Irie; Archie‘s best friend Samad, a Bengali refugee, also married to a woman far younger, Alsana; and their twins, Millat and Majid, mixes them up in a tale of cloning, animal rights, race, Islamic and Christian fundamentalism, and rumours of the end of the world, and places them in Willesden, northwest London, where Smith grew up.