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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, loge x, or sometimes, if the base e is implicit, simply log x.
Log-normal distribution. 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.
Euler's constant (sometimes called the Euler–Mascheroni constant) is a mathematical constant, usually denoted by the lowercase Greek letter gamma ( γ ), defined as the limiting difference between the harmonic series and the natural logarithm, denoted here by log : Here, ⌊·⌋ represents the floor function .
The decimal value of the natural logarithm of 2 (sequence A002162 in the OEIS ) is approximately. The logarithm of 2 in other bases is obtained with the formula. The common logarithm in particular is ( OEIS : A007524 ) The inverse of this number is the binary logarithm of 10: ( OEIS : A020862 ). By the Lindemann–Weierstrass theorem, the ...
In mathematics, the logarithm is the inverse function to exponentiation. 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 = 103, the logarithm base of 1000 is 3, or log10 (1000) = 3.
Overleaf is a collaborative cloud-based LaTeX editor used for writing, editing and publishing scientific documents. [1] [2] It partners with a wide range of scientific publishers to provide official journal LaTeX templates, and direct submission links.
Calculus. In mathematics, specifically in calculus and complex analysis, the logarithmic derivative of a function f is defined by the formula. where is the derivative of f. [1] Intuitively, this is the infinitesimal relative change in f; that is, the infinitesimal absolute change in f, namely scaled by the current value of f.
Logarithmically concave function. In convex analysis, a non-negative function f : Rn → R+ is logarithmically concave (or log-concave for short) if its domain is a convex set, and if it satisfies the inequality. for all x,y ∈ dom f and 0 < θ < 1. If f is strictly positive, this is equivalent to saying that the logarithm of the function, log ...