Logarithm
- 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;
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- To change logarithm base;
- Logarithms are used to simplify multiplication, division and exponentiation.
- For example;
- Examples
- log10(2) = 0.301029995664
- log10(3) = 0.477121254720
- log10(e) = 0.434294481903
- log10(π) = 0.497149872694
- log10(3) = 0.477121254720
- loge(2) = ln(2) = 0.693147180560
- loge(3) = ln(3) = 1.098612288668
- loge(10) = ln(10) = 2.302585092994
- loge(3) = ln(3) = 1.098612288668
Subjects: Algebra