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