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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.
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.
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]
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.
A page from Henry Briggs' 1617 Logarithmorum Chilias Prima showing the base-10 (common) logarithm of the integers 0 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.
The following is a list of integrals (antiderivative functions) of logarithmic functions. For a complete list of integral functions, see list of integrals. Note: x > 0 is assumed throughout this article, and the constant of integration is omitted for simplicity.
This list of mathematical series contains formulae for finite and infinite sums. It can be used in conjunction with other tools for evaluating sums. Here, is taken to have the value
This is a list of limits for common functions such as elementary functions. In this article, the terms a , b and c are constants with respect to x . Limits for general functions
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