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The logarithm keys (LOG for base 10 and LN for base e) on a TI-83 Plus graphing calculator. Logarithms are easy to compute in some cases, such as log 10 (1000) = 3. In general, logarithms can be calculated using power series or the arithmetic–geometric mean, or be retrieved from a precalculated logarithm table that provides a fixed precision.
Discrete logarithm. The problem of inverting exponentiation in finite groups. In mathematics, for given real numbers a and b, the logarithm log b a is a number x such that bx = a. Analogously, in any group G, powers bk can be defined for all integers k, and the discrete logarithm log b a is an integer k such that bk = a.
Common logarithm. A graph of the common logarithm of numbers from 0.1 to 100. In mathematics, the common logarithm is the logarithm with base 10. [1] It is also known as the decadic logarithm and as the decimal logarithm, named after its base, or Briggsian logarithm, after Henry Briggs, an English mathematician who pioneered its use, as well as ...
Binary logarithm. Graph of log2 x as a function of a positive real number x. In mathematics, the binary logarithm (log2 n) is the power to which the number 2 must be raised to obtain the value n. That is, for any real number x, For example, the binary logarithm of 1 is 0, the binary logarithm of 2 is 1, the binary logarithm of 4 is 2, and the ...
The history of logarithms is the story of a correspondence (in modern terms, a group isomorphism) between multiplication on the positive real numbers and addition on the real number line that was formalized in seventeenth century Europe and was widely used to simplify calculation until the advent of the digital computer.
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].
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. The goal is to compute such that , where belongs to a cyclic group generated by . The algorithm computes integers , , , and such that .
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 ...