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DistroKid, formerly titled Fandalism, is an independent digital music distribution service, founded in 2013 by American entrepreneur Philip J. Kaplan. DistroKid principally offers musicians and other rights-holders the opportunity to distribute and sell or stream their music through online retailers such as iTunes / Apple Music , Spotify ...
In probability and statistics, the logarithmic distribution (also known as the logarithmic series distribution or the log-series distribution) is a discrete probability distribution derived from the Maclaurin series expansion = + + +.
The logarithm is denoted "log b x" (pronounced as "the logarithm of x to base b", "the base-b logarithm of x", or most commonly "the log, base b, of x "). An equivalent and more succinct definition is that the function log b is the inverse function to the function x ↦ b x {\displaystyle x\mapsto b^{x}} .
In 1815, Peter Mark Roget invented the log log slide rule, which included a scale displaying the logarithm of the logarithm. This allowed the user to directly perform calculations involving roots and exponents.
In computer science, the iterated logarithm of , written log * (usually read "log star"), is the number of times the logarithm function must be iteratively applied before the result is less than or equal to . The simplest formal definition is the result of this recurrence relation:
The identities of logarithms can be used to approximate large numbers. Note that log b (a) + log b (c) = log b (ac), where a, b, and c are arbitrary constants. Suppose that one wants to approximate the 44th Mersenne prime, 2 32,582,657 −1. To get the base-10 logarithm, we would multiply 32,582,657 by log 10 (2), getting 9,808,357.09543 ...
In probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed. Thus, if the random variable X is log-normally distributed, then Y = ln( X ) has a normal distribution.
Calculus. In calculus, logarithmic differentiation or differentiation by taking logarithms is a method used to differentiate functions by employing the logarithmic derivative of a function f, [1] The technique is often performed in cases where it is easier to differentiate the logarithm of a function rather than the function itself.
The natural logarithm of x is the power to which e would have to be raised to equal x. For example, ln 7.5 is 2.0149..., because e2.0149... = 7.5. The natural logarithm of e itself, ln e, is 1, because e1 = e, while the natural logarithm of 1 is 0, since e0 = 1 .
A logarithmic pair, or log pair for short, is a pair (X,D) consisting of a normal variety X and a boundary Q-divisor D. The log canonical divisor of a log pair (X,D) is K+D where K is the canonical divisor of X.
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