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Logarithm
LogarithmIn the 1500s and early 1600s, although science, engineering, and medicine were flourishing, many people did not understand multiplication tables. Mathematicians, astronomers, navigators, and scientists were forced to spend a lot of time performing calculations, so that little time was left to work on experiments and new discoveries. Finally, around 1594 Scottish mathematician John Napier (1550–1617) produced a table of logarithmic, or proportionate, numbers. How logarithms workIn the commonly known base 10 system, computations that involve very large numbers can become difficult, if not incomprehensible. Napier realized numbers could be more easily expressed in terms of powers. Thus 100 is equal to 10 multiplied by 10, written as 102. This is read as "10 squared" and means "10 to the power two." To perform multiplication, numbers are converted into logarithms, the exponents added together, and the result converted back into base 10. Likewise, to perform division, two logarithmic exponents are subtracted, and the result converted back to base 10. This innovative way of multiplying and dividing large numbers was a milestone event for mathematicians of the day. Napier's tables were published in 1614 and were put into use immediately, becoming an essential part of the mathematical, scientific, and navigational processes. Logarithmic tables remained popular throughout the next several centuries and were used as the basis for many mechanical calculating devices. Relieved from much of their mental drudgery, scientists and mathematicians enjoyed new freedom in their work, allowing them to focus their attention on new scientific breakthroughs. |
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"Logarithm." UXL Encyclopedia of Science. 2002. Encyclopedia.com. 1 Jun. 2012 <http://www.encyclopedia.com>. "Logarithm." UXL Encyclopedia of Science. 2002. Encyclopedia.com. (June 1, 2012). http://www.encyclopedia.com/doc/1G2-3438100397.html "Logarithm." UXL Encyclopedia of Science. 2002. Retrieved June 01, 2012 from Encyclopedia.com: http://www.encyclopedia.com/doc/1G2-3438100397.html |
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logarithm
logarithm [Gr.,=relation number], number associated with a positive number, being the power to which a third number, called the base, must be raised in order to obtain the given positive number. For example, the logarithm of 100 to the base 10 is 2, written log 10 100=2, since 10 2 =100. Logarithms of positive numbers using the number 10 as the base are called common logarithms; those using the number e (see separate article) as the base are called natural logarithms or Napierian logarithms (for John Napier ). The natural logarithm of a number x is denoted by ln x or simply log x. Since logarithms are exponents , they satisfy all the usual rules of exponents. Consequently, tedious calculations such as multiplications and divisions can be replaced by the simpler processes of adding or subtracting the corresponding logarithms. Logarithmic tables are generally used for this purpose. |
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"logarithm." The Columbia Encyclopedia, 6th ed.. 2011. Encyclopedia.com. 1 Jun. 2012 <http://www.encyclopedia.com>. "logarithm." The Columbia Encyclopedia, 6th ed.. 2011. Encyclopedia.com. (June 1, 2012). http://www.encyclopedia.com/doc/1E1-logarith.html "logarithm." The Columbia Encyclopedia, 6th ed.. 2011. Retrieved June 01, 2012 from Encyclopedia.com: http://www.encyclopedia.com/doc/1E1-logarith.html |
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logarithm
logarithm Aid to calculation devised by John Napier in 1614, and developed by the English mathematician Henry Briggs. A number's logarithm is the power to which a base must be raised to equal the number, i.e. if bx = n, then logb n = x, where n is the number, b the base and x the logarithm. Common logarithms have base 10, and so-called natural logarithms have base e (2.71828…). Logarithms to the base 2 are used in computer science and information theory.
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"logarithm." World Encyclopedia. 2005. Encyclopedia.com. 1 Jun. 2012 <http://www.encyclopedia.com>. "logarithm." World Encyclopedia. 2005. Encyclopedia.com. (June 1, 2012). http://www.encyclopedia.com/doc/1O142-logarithm.html "logarithm." World Encyclopedia. 2005. Retrieved June 01, 2012 from Encyclopedia.com: http://www.encyclopedia.com/doc/1O142-logarithm.html |
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logarithm
log·a·rithm / ˈlôgəˌri[voicedth]əm; ˈlägə-/ (abbr.: log) • n. a quantity representing the power to which a fixed number (the base) must be raised to produce a given number. |
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"logarithm." The Oxford Pocket Dictionary of Current English. 2009. Encyclopedia.com. 1 Jun. 2012 <http://www.encyclopedia.com>. "logarithm." The Oxford Pocket Dictionary of Current English. 2009. Encyclopedia.com. (June 1, 2012). http://www.encyclopedia.com/doc/1O999-logarithm.html "logarithm." The Oxford Pocket Dictionary of Current English. 2009. Retrieved June 01, 2012 from Encyclopedia.com: http://www.encyclopedia.com/doc/1O999-logarithm.html |
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logarithm
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T. F. HOAD. "logarithm." The Concise Oxford Dictionary of English Etymology. 1996. Encyclopedia.com. 1 Jun. 2012 <http://www.encyclopedia.com>. T. F. HOAD. "logarithm." The Concise Oxford Dictionary of English Etymology. 1996. Encyclopedia.com. (June 1, 2012). http://www.encyclopedia.com/doc/1O27-logarithm.html T. F. HOAD. "logarithm." The Concise Oxford Dictionary of English Etymology. 1996. Retrieved June 01, 2012 from Encyclopedia.com: http://www.encyclopedia.com/doc/1O27-logarithm.html |
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logarithm
logarithm •hansom, ransom, Ransome, transom
•Wrexham • sensum • Epsom • jetsam
•lissom • winsome • gypsum • alyssum
•blossom, opossum, possum
•flotsam • awesome • balsam • Folsom
•noisome • twosome
•fulsome • buxom • Hilversum
•irksome • Gresham • meerschaum
•petersham • nasturtium
•atom, Euratom
•factum
•bantam, phantom
•sanctum
•desideratum, erratum, post-partum, stratum
•substratum • rectum • momentum
•septum
•datum, petrolatum, pomatum, Tatum, ultimatum
•arboretum • dictum • symptom
•ad infinitum
•bottom, rock-bottom
•quantum
•autumn, postmortem
•factotum, Gotham, scrotum, teetotum, totem
•sputum
•accustom, custom
•diatom • anthem • Bentham • Botham
•fathom • rhythm • biorhythm
•algorithm • logarithm • sempervivum
•ovum • William
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"logarithm." Oxford Dictionary of Rhymes. 2007. Encyclopedia.com. 1 Jun. 2012 <http://www.encyclopedia.com>. "logarithm." Oxford Dictionary of Rhymes. 2007. Encyclopedia.com. (June 1, 2012). http://www.encyclopedia.com/doc/1O233-logarithm.html "logarithm." Oxford Dictionary of Rhymes. 2007. Retrieved June 01, 2012 from Encyclopedia.com: http://www.encyclopedia.com/doc/1O233-logarithm.html |
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