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The logarithm of a number or variable x to base b, logb x, is the exponent of b needed to give x. The bases most commonly used in mathematics are e and 10. A logarithm to base e, written as log x or ln x, is known as a natural logarithm. (For example, loge10 is approximately 2.30258.) A logarithm to base 10 is written as log10 x and is known as a common logarithm.

Since a0 = 1 for any a; log 1 = 0 for all bases. In order to multiply two numbers together, one uses the fact that ax.ay = ax + y, and hence log (x.y) = log x + log y. We therefore look up the values of log x and log y in logarithmic tables, add these values, and then use the tables again to find the number whose logarithm is equal to the result of the addition. Similarly, since ax/ay = ax = y = log(x/y); and since (ax)y = axy, log xy = y.log x. Logx x = 1 since x1 = x.

The antilogarithm of a number x is the number whose logarithm is x; that is, if log y = x, then y is the antilogarithm of x.

A logarithmic curve is the plotting of a function of the form f(x) = log x (i.e., a logarithmic function).

Logarithms, as an aid to calculation, were introduced by John Napier in 1614 and developed by Henry Briggs

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