lecture 4.3 beta bt
TRANSCRIPT
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Today’s Agenda
Attendance / Announcements
Section 4.3
Quiz on Tuesday
Exam 3 (Chapter 4)
Fri 11/1
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The problem…
Solve: x53
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What about…
Solve: 53 x
x1412
216 x
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We need to apply the same idea to exponential
equations, but what is the inverse?
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Logarithms are another way to write exponents
xyby b
x logExponential Form Logarithmic Form
29log3
4log161
2
01log5
38log21
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Logarithms are another way to write exponents
xyby b
x logExponential Form Logarithmic Form
2636
21
819
3
81 2
01 e
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Evaluating Logarithms
xyby b
x logExponential Form Logarithmic Form
)16(log 2
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Evaluating Logarithms
xyby b
x logExponential Form Logarithmic Form
)1(log 5
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Evaluating Logarithms
xyby b
x logExponential Form Logarithmic Form
)1000(log10
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Evaluating Logarithms
xyby b
x logExponential Form Logarithmic Form
)3(log9
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Properties of Logs (pg. 235)
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Two Special Logarithms
The Common Logarithm
10loglog"" means
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Two Special Logarithms
The Common Logarithm
)100log( )15log(
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Two Special Logarithms
The Natural Logarithm
emeans logln""
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Two Special Logarithms
The Natural Logarithm
)2ln( )0ln(
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Two Special Logarithms
The Natural Logarithm
)2ln( )5.3ln(
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Evaluating Logs with Calculator
)8(log3
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Evaluating Logs with Calculator
)8(log3
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More Properties of Logs (pg. 236)
We use these properties to “expand” and “condense” logarithmic expressions.
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More Properties of Logs (pg. 236)
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Expand the following logarithmic expressions
)5log( 2 yx
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Expand the following logarithmic expressions
z
yx2
ln
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Expand the following logarithmic expressions
yz
x5log3
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Condense the following logarithmic expressions
yx ln3lnln2
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Condense the following logarithmic expressions
zyx log4log2log3
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Condense the following logarithmic expressions
2ln4ln2 xx
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Classwork / Homework