Search results
Results from the WOW.Com Content Network
In mathematics, the logarithm to base b is the inverse function of exponentiation with base b. That means that 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 = 10 3, the logarithm base of 1000 is 3, or log 10 (1000) = 3.
The use of log probabilities improves numerical stability, when the probabilities are very small, because of the way in which computers approximate real numbers. [1] Simplicity. Many probability distributions have an exponential form. Taking the log of these distributions eliminates the exponential function, unwrapping the exponent.
The natural logarithm of a number is its logarithm to the base of the mathematical constant e, which is an irrational and transcendental number approximately equal to 2.718 281 828 459. [1] The natural logarithm of x is generally written as ln x , log e x , or sometimes, if the base e is implicit, simply log x .
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 ...
A graph of the common logarithm of numbers from 0.1 to 100. In mathematics, the common logarithm (aka "standard logarithm") is the logarithm with base 10. [1] It is also known as the decadic logarithm, the decimal logarithm and the Briggsian logarithm.
A familiar example of logarithmic growth is a number, N, in positional notation, which grows as log b (N), where b is the base of the number system used, e.g. 10 for decimal arithmetic. [3] In more advanced mathematics, the partial sums of the harmonic series
Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!
The height of the tree (number of rounds of the tournament) is the binary logarithm of the number of players, rounded up to an integer. Although the natural logarithm is more important than the binary logarithm in many areas of pure mathematics such as number theory and mathematical analysis , [ 27 ] the binary logarithm has several ...