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Logarithms and its Real Life Application Chua Cong Yang 3S2’03.

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Presentation on theme: "Logarithms and its Real Life Application Chua Cong Yang 3S2’03."— Presentation transcript:

1 Logarithms and its Real Life Application Chua Cong Yang 3S2’03

2 Content  Definition  Examples  History  Logarithm Identities  Real Life application of logarithms to different fields Chemistry Quantifying Decibels Richter scale Copyright 2008 PresentationFx.com | Redistribution Prohibited | Image © 2008 Thomas Brian | This text section may be deleted for presentation.PresentationFx.com

3 Definition  The logarithm of a number y with respect to base b is the exponent to which b has to be raised in order to yield y  For example: b x = y Can be expressed as: log b y= x Copyright 2008 PresentationFx.com | Redistribution Prohibited | Image © 2008 Thomas Brian | This text section may be deleted for presentation.PresentationFx.com

4 Examples Some examples on logarithms: 10 3 = 1000 Can be expressed as: Log 10 1000 = 3 Copyright 2008 PresentationFx.com | Redistribution Prohibited | Image © 2008 Thomas Brian | This text section may be deleted for presentation.PresentationFx.com

5 History Logarithms was first introduced by John Napier in the early 17th century as a method to simplify calculations and large indices. However, logarithms has been rapidly developed and used in many fields of science now. Copyright 2008 PresentationFx.com | Redistribution Prohibited | Image © 2008 Thomas Brian | This text section may be deleted for presentation.PresentationFx.com

6 History Before the invention of calculators, math has to be done by hand. The invention of logarithms has simplified the common expressions of addition, subtraction, power and root Copyright 2008 PresentationFx.com | Redistribution Prohibited | Image © 2008 Thomas Brian | This text section may be deleted for presentation.PresentationFx.com

7 History In addition, logarithms continues to be used in our lives today. The volume of music is based on the logarithmic scale, the magnitude of an earthquake is also based on a logarithmic scale. Logarithm is widely applied in our lives. Copyright 2008 PresentationFx.com | Redistribution Prohibited | Image © 2008 Thomas Brian | This text section may be deleted for presentation.PresentationFx.com

8 Logarithm Identities Copyright 2008 PresentationFx.com | Redistribution Prohibited | Image © 2008 Thomas Brian | This text section may be deleted for presentation.PresentationFx.com Identities Power Law Product Law Quotient Law Change of Base Law

9 Power Law Copyright 2008 PresentationFx.com | Redistribution Prohibited | Image © 2008 Thomas Brian | This text section may be deleted for presentation.PresentationFx.com

10 Product Law Copyright 2008 PresentationFx.com | Redistribution Prohibited | Image © 2008 Thomas Brian | This text section may be deleted for presentation.PresentationFx.com

11 Quotient Law Copyright 2008 PresentationFx.com | Redistribution Prohibited | Image © 2008 Thomas Brian | This text section may be deleted for presentation.PresentationFx.com

12 Change of Base Law Copyright 2008 PresentationFx.com | Redistribution Prohibited | Image © 2008 Thomas Brian | This text section may be deleted for presentation.PresentationFx.com

13 Change of Base Law Copyright 2008 PresentationFx.com | Redistribution Prohibited | Image © 2008 Thomas Brian | This text section may be deleted for presentation.PresentationFx.com

14 Real Life Applications of Logarithms Copyright 2008 PresentationFx.com | Redistribution Prohibited | Image © 2008 Thomas Brian | This text section may be deleted for presentation.PresentationFx.comApplications Richter Scale Chemistry Sound

15 Chemistry Copyright 2008 PresentationFx.com | Redistribution Prohibited | Image © 2008 Thomas Brian | This text section may be deleted for presentation.PresentationFx.com

16 Chemistry Copyright 2008 PresentationFx.com | Redistribution Prohibited | Image © 2008 Thomas Brian | This text section may be deleted for presentation.PresentationFx.com

17 Sounds

18 Sounds

19 Richter Scale Copyright 2008 PresentationFx.com | Redistribution Prohibited | Image © 2008 Thomas Brian | This text section may be deleted for presentation.PresentationFx.com

20 References- Pictures http://www.daviddarling.info/images/Napier.jpg http://s3.amazonaws.com/pixmac-preview/math-and- science-symbols-background.jpghttp://s3.amazonaws.com/pixmac-preview/math-and- science-symbols-background.jpg http://upload.wikimedia.org/wikipedia/commons/thumb/f/f 9/LinLinScale.png/600px-LinLinScale.pnghttp://upload.wikimedia.org/wikipedia/commons/thumb/f/f 9/LinLinScale.png/600px-LinLinScale.png http://upload.wikimedia.org/math/1/3/e/13e5e0759d863fb b88d35d2ca1421b7b.pnghttp://upload.wikimedia.org/math/1/3/e/13e5e0759d863fb b88d35d2ca1421b7b.png http://www.genexusa.com/images/misc/decibels.jpg Copyright 2008 PresentationFx.com | Redistribution Prohibited | Image © 2008 Thomas Brian | This text section may be deleted for presentation.PresentationFx.com

21 References -Text http://wiki.answers.com/Q/How_can_logarithms_relate_to_ever yday_livinghttp://wiki.answers.com/Q/How_can_logarithms_relate_to_ever yday_living http://en.wikipedia.org/wiki/Logarithm#Definition http://wiki.answers.com/Q/An_example_how_logarithms_are_u sed_to_explain_a_real_life_occurancehttp://wiki.answers.com/Q/An_example_how_logarithms_are_u sed_to_explain_a_real_life_occurance http://www.uiowa.edu/~examserv/mathmatters/tutorial_quiz/log _exp/realworldappslogarithm.htmlhttp://www.uiowa.edu/~examserv/mathmatters/tutorial_quiz/log _exp/realworldappslogarithm.html http://en.wikipedia.org/wiki/Logarithmic_scale http://samjshah.com/2008/07/30/earthquakes-richter-scale- and-logarithms/http://samjshah.com/2008/07/30/earthquakes-richter-scale- and-logarithms/ Copyright 2008 PresentationFx.com | Redistribution Prohibited | Image © 2008 Thomas Brian | This text section may be deleted for presentation.PresentationFx.com

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