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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.
In mathematics, for given real numbers a and b, the logarithm log b a is a number x such that b x = a.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.
The iterated logarithm is closely related to the generalized logarithm function used in symmetric level-index arithmetic.The additive persistence of a number, the number of times someone must replace the number by the sum of its digits before reaching its digital root, is ().
The exponential of a matrix A is defined by =!. Given a matrix B, another matrix A is said to be a matrix logarithm of B if e A = B.. Because the exponential function is not bijective for complex numbers (e.g. = =), numbers can have multiple complex logarithms, and as a consequence of this, some matrices may have more than one logarithm, as explained below.
The law of iterated logarithms operates "in between" the law of large numbers and the central limit theorem.There are two versions of the law of large numbers — the weak and the strong — and they both state that the sums S n, scaled by n −1, converge to zero, respectively in probability and almost surely:
Henry Briggs (1 February 1561 – 26 January 1630) was an English mathematician notable for changing the original logarithms invented by John Napier into common (base 10) logarithms, which are sometimes known as Briggsian logarithms in his honour.
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 planned date for the formation of the new federation was 1 June 1963, but the event was postponed to 31 August 1963, to coincide with the sixth anniversary of Hari Merdeka. Several issues relating to the objections of neighbouring Indonesia and the Philippines to the formation of Malaysia delayed the declaration to 16 September of the same year