logarithm

logarithm [Gr.,=relation number], number associated with a positive number, being the power to which a third number, called the base, must be raised in order to obtain the given positive number. For example, the logarithm of 100 to the base 10 is 2, written log ₁₀ 100=2, since 10 ² =100. Logarithms of positive numbers using the number 10 as the base are called common logarithms; those using the number e (see separate article) as the base are called natural logarithms or Napierian logarithms (for John Napier). The natural logarithm of a number x is denoted by ln x or simply log x. Since logarithms are exponents , they satisfy all the usual rules of exponents. Consequently, tedious calculations such as multiplications and divisions can be replaced by the simpler processes of adding or subtracting the corresponding logarithms. Logarithmic tables are generally used for this purpose.

logarithm Aid to calculation devised by John Napier in 1614, and developed by the English mathematician Henry Briggs. A number's logarithm is the power to which a base must be raised to equal the number, i.e. if b^x = n, then log_b n = x, where n is the number, b the base and x the logarithm. Common logarithms have base 10, and so-called natural logarithms have base e (2.71828…). Logarithms to the base 2 are used in computer science and information theory.