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e. 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 = 103, the logarithm base of 1000 is 3, or log10 (1000) = 3.
The natural logarithm of e itself, ln e, is 1, because e1 = e, while the natural logarithm of 1 is 0, since e0 = 1. The natural logarithm can be defined for any positive real number a as the area under the curve y = 1/x from 1 to a[4] (with the area being negative when 0 < a < 1). The simplicity of this definition, which is matched in many ...
ln (r) is the standard natural logarithm of the real number r. Arg (z) is the principal value of the arg function; its value is restricted to (−π, π]. It can be computed using Arg (x + iy) = atan2 (y, x). Log (z) is the principal value of the complex logarithm function and has imaginary part in the range (−π, π].
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. [2][3] Equivalently, if Y has a normal distribution, then the exponential ...
Logarithmic scale. A logarithmic scale (or log scale) is a method used to display numerical data that spans a broad range of values, especially when there are significant differences between the magnitudes of the numbers involved. Unlike a linear scale where each unit of distance corresponds to the same increment, on a logarithmic scale each ...
a.e. – almost everywhere. AFSOC - Assume for the sake of contradiction. Ai – Airy function. AL – Action limit. Alt – alternating group (Alt (n) is also written as A n.) A.M. – arithmetic mean. AP – arithmetic progression. arccos – inverse cosine function. arccosec – inverse cosecant function.
A square root of a number x is a number r which, when squared, becomes x: =. Every positive real number has two square roots, one positive and one negative. For example, the two square roots of 25 are 5 and −5. The positive square root is also known as the principal square root, and is denoted with a radical sign:
The symbol # is known variously in English-speaking regions as the number sign, [1] hash, [2] or pound sign. [3] The symbol has historically been used for a wide range of purposes including the designation of an ordinal number and as a ligatured abbreviation for pounds avoirdupois – having been derived from the now-rare ℔ .
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