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Line 1: − A '''logarithm''' of a [[number]] is the [[exponential]] power to which you raise the base to obtain the number.+ + − + Line 13:
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Note error in image
[[Image:log.png|thumb|right|px=200|Logarithm with various bases. Note that the legend has an error: it confuses the base 2 and base e lines.]]
'''Logarithm''' of a [[number]] is the [[exponential]] power to which you raise the base to obtain the number.
For high school [[algebra]], the most common base is "10".
For high school [[algebra]], the most common logarithms are base-10 (the common log) and base ''[[e]]'' (the [[natural logarithm|natural log]]).
For example, the logarithm base 10 of 100 is the power to which you raise 10 to obtain 100. Because 10 to the power of 2 equals 100, the logarithm of 100 is 2:
For example, the logarithm base 10 of 100 is the power to which you raise 10 to obtain 100. Because 10 to the power of 2 equals 100, the logarithm of 100 is 2:
==History==
==History==
Logarithms were used for centuries as a computing tool by [[scientist]]s making pencil-and-paper [[computation]]s.
Logarithms were used for centuries as a computing tool by [[scientist]]s making pencil-and-paper [[computation]]s, because the use of logarithms can greatly simplify arithmetical calculations. For example, raising a number x to any power y (where x and y might be large or fractional) can be achieved by first looking up the logarithm of x, then multiplying by y, and then finding the inverse logarithm of the result.
Logarithms were invented or discovered by [[John Napier]] in 1614 AD, and quickly revolutionized astronomy. Johannes Kepler said that Napier "tripled the life of an astronomer."
Logarithms were invented or discovered by [[John Napier]] in 1614 AD, and quickly revolutionized astronomy. Johannes Kepler said that Napier "tripled the life of an astronomer."
The arrival of pocket-sized electronic [[calculator]]s brought an end to the practical use of the slide rule or the table of logarithms. A calculator can compute a logarithm to ten places in less time than it takes to turn to the right page in a book-sized table of logarithms.
The arrival of pocket-sized electronic [[calculator]]s brought an end to the practical use of the slide rule or the table of logarithms. A calculator can compute a logarithm to ten places in less time than it takes to turn to the right page in a book-sized table of logarithms.
[[category:mathematics]]
[[Category:Mathematics]]