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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.
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The Swiss mathematician Jost Bürgi constructed a table of progressions which can be considered a table of antilogarithms [25] independently of John Napier, whose publication (1614) was known by the time Bürgi published at the behest of Johannes Kepler. We know that Bürgi had some way of simplifying calculations around 1588, but most likely ...
Using logarithm tables, tedious multi-digit multiplication steps can be replaced by table look-ups and simpler addition. This is possible because the logarithm of a product is the sum of the logarithms of the factors: log b ( x y ) = log b x + log b y , {\displaystyle \log _{b}(xy)=\log _{b}x+\log _{b}y,} provided that b , x and y ...
Semi-log plot of the Internet host count over time shown on a 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.
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.
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 . v
Blackmer reasoned that the log-antilog detector may be simplified by taking up processing to log domain, omitting physical squaring of input signals and thus retaining its full dynamic range. [3] Squaring and taking square roots in log domain is very cheap, being simple scaling by a factor of 2 or 1/2. [7]