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)

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