Mathematical tables are lists of numbers showing the results of a calculation with varying arguments. Trigonometric tables were used in ancient Greece and India for applications to astronomy and celestial navigation, and continued to be widely used until electronic calculators became cheap and plentiful in the 1970s, in order to simplify and drastically speed up computation. Tables of logarithms and trigonometric functions were common in math and science textbooks, and specialized tables were published for numerous applications.
These mathematical tables from 1925 were distributed by the College Entrance Examination Board to students taking the mathematics portions of the tests
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.
Image: Bernegger Manuale 136
In mathematics, the logarithm is the inverse function to exponentiation. 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 = 103, the logarithm base of 1000 is 3, or log10 (1000) = 3. The logarithm of x to base b is denoted as logb (x), or without parentheses, logb x. When the base is clear from the context or is irrelevant, such as in big O notation, it is sometimes written log x.
The logarithm keys (LOG for base 10 and LN for base e) on a TI-83 Plus graphing calculator
A nautilus shell displaying a logarithmic spiral