logarithm

Definition von logarithm im Englisch Englisch wörterbuch: For a number x, the power to which a given base number must be raised in order to obtain x. Written \log_b x. For example, \log_{10} 1000 = 3 because 10^3 = 1000 and \log_2 16 = 4 because 2^4 = 16; It is helpful to think of "power " Thus 103 = 1000 and log (1000) = 3 This is another source of confusion in acid base balance and is responsible for the mistaken impression that the body maintains remarkably tight control over its hydrogen ion concentration (Blood pressure or pulse measured with a logarithmic notation would also appear remarkably stable) When the pH changes by 0 3 units, e g , from 7 4 to 7 1 the hydrogen ion concentration doubles (from 40 to 80 nmol/1 ); The inverse of exponentiation; for example, alogax = x (Remember that logarithm is an operation like addition or exponentiation ); An exponent used in mathematical equations to express the level of a variable quantity (or, the power to which a number must be raised to produce a specific result); The inverse function of an exponential For example ln(ex)=x=eln(x), for x>0; For a number x, the power to which a given base number must be raised in order to obtain x. Written log_b x. For example, log_{10} 1000 = 3 because 10^3 = 1000; Exponent of the power to which it is necessary to raise a fixed number (the base) to produce the given number For example, the logarithm of 100 (base 10) is 2 because 102 equals 100; The exponent expressing the power to which a fixed number must be raised to produce a given number; One of a class of auxiliary numbers, devised by John Napier, of Merchiston, Scotland (1550-1617), to abridge arithmetical calculations, by the use of addition and subtraction in place of multiplication and division; Thus, the common logarithm of 100 (log 100) is 2, because 10^2 = 100. Logarithms to the base e, in which e = 2.71828..., called natural logarithms (ln), are especially useful in calculus. Logarithms were invented to simplify cumbersome calculations, since exponents can be added or subtracted to multiply or divide their bases. These processes have been further simplified by the incorporation of logarithmic functions into digital calculators and computers. See also John Napier; The exponent of the power to which a base number must be raised to equal a given number An example: 2 is the logarithm of 100 to the base 10 One can look at this way: 10 * 10 = 100, which is the same as 102, and 2 is the exponent referred to above (cfExponents and Logarithms Discussion and Trees as Data Structures Discussion); the power to which a number is raised -- the exponent Example: log 10^2 = 2; In the equation a=bx, the logarithm base b of a provides the value of the exponent, logba=x The logarithm is the exponent that is put on b to give the value of a; The exponent that indicates the power to which a number must be raised to produce a given number For example: if B2 = N, the 2 is the logarithm of N (to the base B), or 102 =100 and log10 100 = 2 Also abbreviated to "log "; the exponent required to produce a given number; 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. a number representing another number in a mathematical system so that complicated calculations can be done as simple addition (logarithmus, from logos ( LOGIC) + arithmos ). In mathematics, the power to which a base must be raised to yield a given number (e.g., the logarithm to the base 3 of 9, or log3 9, is 2, because 3^2 = 9). A common logarithm is a logarithm to the base; {i} power to which a base must be raised to produce a given number (Mathematics)
logarithm table: table used to find a logarithm easily (without calculations)
binary logarithm: The logarithm base two
logarithmic: Of, or relating to logarithms
natural logarithm: The logarithm in base e; either the function that given x\! returns y\! such that e^y = x\! or the value of y\!
The natural logarithm can be used to integrate 1/x.
logarithms: {n} the indexes of the ratios of numbers to each other
A logarithm: log
Logarithmically: logarithmetically
common logarithm: logarithm with the number ten as its base (Mathematics)
common logarithm: A logarithm to the base 10, especially as distinguished from a natural logarithm
common logarithm: a logarithm to the base 10
logarithmic: Of or pertaining to logarithms; consisting of logarithms
logarithmic: of or relating to or using logarithms; "logarithmic function"
logarithmic: of or relating to or using logarithms; "logarithmic function
logarithmic: {s} of or pertaining to logarithms (Mathematics)
logarithmically: In a logarithmic manner
logarithmically: By the use of logarithms
logarithmically: in a logarithmic manner; "data plotted logarithmically with respect to time is shown in Figure 2
logarithmically: by means of logarithms (Mathematics)
logarithms: plural of logarithm
natural logarithm: a logarithm to the base e
natural logarithm: A logarithm in which the base is the irrational number e (= 2.71828...). For example, ln 10 = log10 = approximately 2.30258. Also called Napierian logarithm
natural logarithm: {i} logarithm which has the irrational number "e" as its base (Mathematics)

logarithm

Silbentrennung

log·a·rithm

Türkische aussprache

lägırîdhım

Synonyme

log

Aussprache

/ˈlägərˌəᴛʜəm/ /ˈlɑːɡɜrˌɪðəm/

Etymologie

() From New Latin logarithmus, term coined by Scot mathematician John Napier from Ancient Greek λόγος (logos, “word, reason”) and ἀριθμός (arithmos, “number”).

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