Today’s Agenda
 Attendance

 Section

/ Announcements

4.3
 Quiz on Tuesday
 Exam 3 (Chapter 4)


Fri 11/1
The problem…
Solve:

3 5

x
What about…
Solve:

3 x 5
12 14x
16

x

2
We need to apply the same idea to exponential
equations, but what is the inverse?
Logarithms are another way to write exponents
Exponential Form
x

y

b

Logarithmic Form

log b y

x

log 3 9

2

1
16

lo...
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 Fo...
Evaluating Logarithms
Exponential Form
x

y

b

log 2 (16 )

Logarithmic Form

log b y

x
Evaluating Logarithms
Exponential Form
x

y

b

log 5 (1)

Logarithmic Form

log b y

x
Evaluating Logarithms
Exponential Form
x

y

b

log10 (1000 )

Logarithmic Form

log b y

x
Evaluating Logarithms
Exponential Form
x

y

b

log 9 (3)

Logarithmic Form

log b y

x
Properties of Logs (pg. 235)
Two Special Logarithms
The Common Logarithm

" log" means log10
Two Special Logarithms
The Common Logarithm

log(100)

log(15)
Two Special Logarithms
The Natural Logarithm

" ln" means log e
Two Special Logarithms
The Natural Logarithm

ln(2)

ln(0)
Two Special Logarithms
The Natural Logarithm

ln( 2)

ln( 3.5)
Evaluating Logs with Calculator

log 3 (8)
Evaluating Logs with Calculator

log 3 (8)
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

2

log(5 x y )
Expand the following logarithmic expressions

ln

x

2

y
z
Expand the following logarithmic expressions

5x
log 3
yz
Condense the following logarithmic expressions

2 ln x ln 3 ln y
Condense the following logarithmic expressions

3 log x 2 log y 4 log z
Condense the following logarithmic expressions

2 ln x 4 ln x 2
Classwork / Homework
Lecture 4.3 beta bt
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Lecture 4.3 beta bt

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

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