Allow large number ranges to be expressed over a smaller range of numbers, eg decibel scale. Also, multiplication and division may be expressed as simple addition and subtraction. Invented by Scottish mathematician John Napier in 1614.

The power to which a base must be raised to yield a given number, usually abbreviated to;
where b is the base. Common logarithms have base 10. Natural logarithms have base e, and are usually expressed;

this is termed the antilogarithm of y.
To change logarithm base;

Logarithms are used to simplify multiplication, division and exponentiation.
For example;
log10(2) = 0.301029995664
log10(3) = 0.477121254720
log10(e) = 0.434294481903
log10(π) = 0.497149872694

loge(2) = ln(2) = 0.693147180560
loge(3) = ln(3) = 1.098612288668
loge(10) = ln(10) = 2.302585092994

See also: Exponent, Napier, John, Neper.

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Subjects: Algebra