Day50_LogarithmIntroduction_notes.notebook
Warm­Up
Simplify:
January 16, 2015
3) If you invest $200 at 1% interest compounded monthly, how much will you have after 3 years?
1) 811/4
4) If you have 100 bacteria that increase at a rate of 53% per hour, how much will you have after 2 hours?
2) (196a 6b­2 c)1/2
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Day50_LogarithmIntroduction_notes.notebook
January 16, 2015
Homework
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Day50_LogarithmIntroduction_notes.notebook
January 16, 2015
Solve the following equations:
1) 3x + 1 = 13
2) (x + 2)3 ­ 4 = 4
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Day50_LogarithmIntroduction_notes.notebook
January 16, 2015
Solve the following equations:
1) 2x = 8
2) 10x = 100
3) 10x = 376
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Day50_LogarithmIntroduction_notes.notebook
January 16, 2015
Logarithms
We need something that will help us solve exponential equations. In the past, we have used inverse operations to solve equations so we need to define a new function that is the inverse of an exponential function. We call this type of function a logarithmic function.
Exponential Equation
(Inverse) Logarithmic Equation
10x = y
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Solve the following equations:
1) 10x = 100
2) 10x = √10
3) 10x = 376
4) 10x = 10000
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Day50_LogarithmIntroduction_notes.notebook
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Richter Scale
The Richter magnitude scale , also known as the local magnitude (ML) scale, assigns a single number to quantify the amount of seismic energy released by an earthquake. It is a base­10 logarithmic scale obtained by calculating the logarithm of the combined horizontal amplitude (shaking amplitude) of the largest displacement from zero on a particular type of seismometer (Wood–
Anderson torsion). So, for example, an earthquake that measures 5.0 on the Richter scale has a shaking amplitude 10 times larger than one that measures 4.0. The effective limit of measurement for local magnitude ML is about 6.8.
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April 29, 2003
Just before 5 a.m. a moderate earthquake, rated 4.9 on the Richter Scale, shook most of the northwest corner of Georgia, south to Atlanta. The epicenter was located in Menlo, Georgia, about 37 miles south of Chattanooga.
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Logarithms of another base:
The basic logarithm works well if the problem is base 10. But if we have another base like base 2. We need to make an adjustment.
Exponential Equation
(Inverse) Logarithmic Equation
2x = y
And in general,
bx = y
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Day50_LogarithmIntroduction_notes.notebook
January 16, 2015
Solve the following equations:
1) 2x = 8
2) 2x = 5
3) 2x = 25/4
4) 2x = 1048576
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Day50_LogarithmIntroduction_notes.notebook
January 16, 2015
Solve the following equations:
1) ex = 100
2) ex = 12
3) ex = 376
4) ex = e5
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January 16, 2015
There also is a shortcut for loge which is known as the natural log since it uses
the natural number, e. We sometimes use ln which stands for "logarithm natural" instead.
Solve the following equations:
1) ex = 100
2) ex = 12
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