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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.
Pollard's rho algorithm for logarithms is an algorithm introduced by John Pollard in 1978 to solve the discrete logarithm problem, analogous to Pollard's rho algorithm to solve the integer factorization problem.
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 ...
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 logarithm keys (log for base-10 and ln for base-e) on a typical scientific calculator. The advent of hand-held calculators largely eliminated the use of common logarithms as an aid to computation. The numerical value for logarithm to the base 10 can be calculated with the following identities: [5]
Discrete logarithm records are the best results achieved to date in solving the discrete logarithm problem, which is the problem of finding solutions x to the equation = given elements g and h of a finite cyclic group G.
Dedicated to the discrete logarithm in (/) where is a prime, index calculus leads to a family of algorithms adapted to finite fields and to some families of elliptic curves. The algorithm collects relations among the discrete logarithms of small primes, computes them by a linear algebra procedure and finally expresses the desired discrete ...
The binary logarithm function may be defined as the inverse function to the power of two function, which is a strictly increasing function over the positive real numbers and therefore has a unique inverse. [7]
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