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Lecture 4.3 beta bt
1.
Today’s Agenda Attendance
Section / Announcements 4.3 Quiz on Tuesday Exam 3 (Chapter 4) Fri 11/1
2.
The problem… Solve: 3 5 x
3.
What about… Solve: 3 x
5 12 14x 16 x 2
4.
We need to
apply the same idea to exponential equations, but what is the inverse?
5.
Logarithms are another
way to write exponents Exponential Form x y b Logarithmic Form log b y x log 3 9 2 1 16 log 2 4 log 5 1 0 log 1 8 2 3
6.
Logarithms are another
way to write exponents Exponential Form x y b 36 6 9 81 1 8 2 1 e 2 1 2 3 0 Logarithmic Form log b y x
7.
Evaluating Logarithms Exponential Form x y b log
2 (16 ) Logarithmic Form log b y x
8.
Evaluating Logarithms Exponential Form x y b log
5 (1) Logarithmic Form log b y x
9.
Evaluating Logarithms Exponential Form x y b log10
(1000 ) Logarithmic Form log b y x
10.
Evaluating Logarithms Exponential Form x y b log
9 (3) Logarithmic Form log b y x
11.
Properties of Logs
(pg. 235)
12.
Two Special Logarithms The
Common Logarithm " log" means log10
13.
Two Special Logarithms The
Common Logarithm log(100) log(15)
14.
Two Special Logarithms The
Natural Logarithm " ln" means log e
15.
Two Special Logarithms The
Natural Logarithm ln(2) ln(0)
16.
Two Special Logarithms The
Natural Logarithm ln( 2) ln( 3.5)
17.
18.
Evaluating Logs with
Calculator log 3 (8)
19.
Evaluating Logs with
Calculator log 3 (8)
20.
More Properties of
Logs (pg. 236) We use these properties to “expand” and “condense” logarithmic expressions.
21.
More Properties of
Logs (pg. 236)
22.
Expand the following
logarithmic expressions 2 log(5 x y )
23.
Expand the following
logarithmic expressions ln x 2 y z
24.
Expand the following
logarithmic expressions 5x log 3 yz
25.
Condense the following
logarithmic expressions 2 ln x ln 3 ln y
26.
Condense the following
logarithmic expressions 3 log x 2 log y 4 log z
27.
Condense the following
logarithmic expressions 2 ln x 4 ln x 2
28.
Classwork / Homework
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