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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, log e x, or sometimes, if the base e is implicit, simply log x.
The multiple valued version of log(z) is a set, but it is easier to write it without braces and using it in formulas follows obvious rules. log(z) is the set of complex numbers v which satisfy e v = z; arg(z) is the set of possible values of the arg function applied to z. When k is any integer:
mathematical constant e; Properties; Natural logarithm; Exponential function; Applications; compound interest; Euler's identity; Euler's formula; half-lives. exponential growth and decay; Defining e; proof that e is irrational; representations of e; Lindemann–Weierstrass theorem; People; John Napier; Leonhard Euler; Related topics; Schanuel's ...
The area of the blue region converges to Euler's constant. 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:
A Poisson compounded with Log(p)-distributed random variables has a negative binomial distribution. In other words, if N is a random variable with a Poisson distribution , and X i , i = 1, 2, 3, ... is an infinite sequence of independent identically distributed random variables each having a Log( p ) distribution, then
I think it is a terminology issue, meaning that some people use log for the logarithm in general, while others differentiate between log for base 10 and ln for base e. As you can seen in the logit graph which says f(x) = log(x/(1-x)) it can't be a base 10 logarithm, but is a base e logarithm.
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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}} .