Post on 02-Jan-2016
transcript
Logarithms and its Real Life Application
Chua Cong Yang3S2’03
Content Definition Examples History Logarithm Identities Real Life application of
logarithms to different fields Chemistry Quantifying Decibels Richter scale
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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: logb y= x
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Examples
• Some examples on logarithms:
103 = 1000
Can be expressed as:
Log10 1000 = 3
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History
• Logarithms was first introduced by John Napier in the early 17th century as a method to simplify calculations and large indices.
• However, logarithms hasbeen rapidly developed and used in many fields of science now.
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History
• Before the invention of calculators, math has to be done by hand.
• The invention of logarithmshas simplified the common expressions of addition,subtraction, power androot
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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 appliedin our lives.
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Logarithm Identities
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Identities
PowerLaw
Product Law
Quotient Law
Change of Base Law
Power Law
• Formula:
• Example:
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Product Law
• Formula:
• Example:
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Quotient Law
• Formula:
• Example:
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Change of Base Law
• Formula:
• Example:
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Change of Base Law
• Formula:
• Example:
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Real Life Applications of Logarithms
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Applications
Richter Scale
Chemistry
Sound
Chemistry
• The formula for calculating pH of a solution is:
• Where is the concentration of hydroxide ions
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Chemistry
• Example: If the pH of Hydrochloric acid is 2, what is the concentration of hydroxide ions?
• Solution:
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Sounds
• The formula to calculate the decibels is:
• Where is the number of decibels is the intensity and is the intensity and is the threshold
Sounds
• Find the decibel rating for the sound intensity of 5000
= 36.99
Richter Scale
• Richter magnitudes are determined by the amplitude of the waves made by the seismograph
• The formula for Richter scale is:
• Where is the magnitude and A is the intensity
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References- Pictures• http://www.daviddarling.info/images/Napier.jpg• http://s3.amazonaws.com/pixmac-preview/math-and-sci
ence-symbols-background.jpg• http://upload.wikimedia.org/wikipedia/commons/thumb/f/f
9/LinLinScale.png/600px-LinLinScale.png• http://
upload.wikimedia.org/math/1/3/e/13e5e0759d863fbb88d35d2ca1421b7b.png
• http://www.genexusa.com/images/misc/decibels.jpg
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References -Text
• http://wiki.answers.com/Q/How_can_logarithms_relate_to_everyday_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_occurance• http://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/
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