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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 common logarithm of any given positive number is then obtained by adding its mantissa to the common logarithm of the second factor. This logarithm is called the characteristic of the given number. Since the common logarithm of a power of 10 is exactly the exponent, the characteristic is an integer number, which makes the common
Exponentiation is written as bn, where b is the base and n is the power; this is pronounced as " b (raised) to the (power of) n ". 1 When n is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, bn is the product of multiplying n bases: 1.
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 mathematics and computer programming, the order of operations is a collection of rules that reflect conventions about which operations to perform first in order to evaluate a given mathematical expression. These rules are formalized with a ranking of the operations. The rank of an operation is called its precedence, and an operation with a ...
Inverse of logarithm integral. Define to be the unique number y > 0 such that =. That is, is the inverse of the natural logarithm function = (), which is defined by this integral. Differential equation.
Analogously, in any group G, powers b k can be defined for all integers k, and the discrete logarithm log b a is an integer k such that b k = a. In number theory , the more commonly used term is index : we can write x = ind r a (mod m ) (read "the index of a to the base r modulo m ") for r x ≡ a (mod m ) if r is a primitive root of m and gcd ...
An important property of base-10 logarithms, which makes them so useful in calculations, is that the logarithm of numbers greater than 1 that differ by a factor of a power of 10 all have the same fractional part. The fractional part is known as the mantissa. [note 2] Thus, log tables need only show the fractional part. Tables of common ...
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