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Tables of common logarithms typically listed the mantissa, to four or five decimal places or more, of each number in a range, e.g. 1000 to 9999. The integer part, called the characteristic , can be computed by simply counting how many places the decimal point must be moved, so that it is just to the right of the first significant digit.
These mathematical tables from 1925 were distributed by the College Entrance Examination Board to students taking the mathematics portions of the tests. Tables of common logarithms were used until the invention of computers and electronic calculators to do rapid multiplications, divisions, and exponentiations, including the extraction of nth roots.
Logarithms can be used to make calculations easier. For example, two numbers can be multiplied just by using a logarithm table and adding. These are often known as logarithmic properties, which are documented in the table below. [2] The first three operations below assume that x = b c and/or y = b d, so that log b (x) = c and log b (y) = d.
A page from Henry Briggs' 1617 Logarithmorum Chilias Prima showing the base-10 (common) logarithm of the integers 1 to 67 to fourteen decimal places. Part of a 20th-century table of common logarithms in the reference book Abramowitz and Stegun. A page from a table of logarithms of trigonometric functions from the 2002 American Practical Navigator.
Common logarithms (base 10), historically used in logarithm tables and slide rules, are a basic tool for measurement and computation in many areas of science and engineering; in these contexts log x still often means the base ten logarithm. [10] In mathematics log x usually refers to the natural logarithm (base e). [11]
Milton Abramowitz and Irene A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 1964. A few integrals are listed on page 69
7.5 Exponential and logarithms. 8 See also. 9 Notes. 10 References. Toggle the table of contents. List of mathematical series. 12 languages.
Common logarithm; Complex logarithm; D. ... Logarithm of a matrix; Logarithm table; ... Pollard's rho algorithm for logarithms;