» Part 1
Logarithms initially originated in an early form along of logarithm tables published by the Augustinian Monk Michael Stifel when he published ’Arithmetica integra’ in 1544. In the same publication, Stifel also became the first person to use the word ‘exponent’ and the first to indicate multiplication without the use of a symbol. In addition to mathematical findings, he also later anonymously published his prediction that at 8:00am on the 19th of October 1533, the world would end and it would be judgement day. However the Scottish astronomer, physicist, mathematician and astrologer John Napier is more famously known as the person who discovered them due to his work in 1614 called ‘Mirifici Logarithmorum Canonis Descriptio’. The reason they were created is to present and express numbers in a new form that was easy to work with. He was successful, as logarithms can be applied in many functions which are used commonly today. They were even more useful back around the time they were created however, as there were no calculators in existence. Scientists (astronomers in particular) had to do massive amounts of calculations on paper which was very time consuming and inconvenient. When logarithms were introduced to them, they weren’t obliged to spend so much time on tedious arithmetic. Logarithms are essentially just exponents, as they show values by using a base number that is raised to a given exponent. Stifel created his logarithm tables to change complicated multiplication and division problems into addition and subtraction equations.
» Part 2
Logarithms have the ability to replace a geometric sequence with an arithmetic sequence because they raise a base number by an exponent. A simple example can be provided with a geome...
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...1.254 = 2.4414
(1+1/5)5 = 1.25 = 2.4883
(1+1/10)10 = 1.110 = 2.5937
(1+1/100)100 = 1.01100 = 2.7048
(1+1/1000)1000 = 1.0011000 = 2.7169
(1+1/10000)10000 = 1.000110000 = 2.7181
(1+1/∞)∞ = (1+∞) ∞ = 2.7182818284590452353602874713526624977572470936... = e
Works Cited
http://betterexplained.com/articles/an-intuitive-guide-to-exponential-functions-e/
http://oakroadsystems.com/math/loglaws.htm
http://www.physics.uoguelph.ca/tutorials/LOG/
http://en.wikipedia.org/wiki/Michael_Stifel
http://en.wikipedia.org/wiki/John_Napier
http://www.ndt-ed.org/EducationResources/Math/Math-e.htm
http://www.thocp.net/reference/sciences/mathematics/logarithm_hist.htm
http://mathforum.org/dr.math/faq/faq.pi.html
http://www.recoveredscience.com/constanteofgrowth.htm
http://www.mathworksheetscenter.com/mathtips/logarithms.html
http://www.zyra.org.uk/log-e.htm
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from his tables, which showed powers of 10 with a fixed number used as a base.
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