1. Splash Screen

2. Five-Minute Check (over Lesson 7–3) CCSS Then/Now New Vocabulary
Example 1: Solve a Logarithmic Equation
Key Concept: Property of Equality for Logarithmic Functions
Example 2: Standardized Test Example: Solve a Logarithmic Equation
Key Concept: Property of Inequality for Logarithmic Functions
Example 3: Solve a Logarithmic Inequality
Example 4: Solve Inequalities with Logarithms on Each Side
Lesson Menu

3. Write 4–3 = in logarithmic form.__ 1 64
A. log–3 4 =
B. log– = 4
C. log = –3
D. log4 –3 = __ 1 64
5-Minute Check 1

4. Write 4–3 = in logarithmic form.__ 1 64
A. log–3 4 =
B. log– = 4
C. log = –3
D. log4 –3 = __ 1 64
5-Minute Check 1

5. Write log6 216 = 3 in exponential form.
B. 36 = 216 C. D.
5-Minute Check 2

6. Write log6 216 = 3 in exponential form.
B. 36 = 216 C. D.
5-Minute Check 2

7. Graph f(x) = 2 log2 x. C. D.
A. ans
B. ans
5-Minute Check 3

8. Graph f(x) = 2 log2 x. C. D.
A. ans
B. ans
5-Minute Check 3

9. Graph f(x) = log3 (x – 4). A. B. C. D.
5-Minute Check 4

10. Graph f(x) = log3 (x – 4). A. B. C. D.
5-Minute Check 4

11. A. B. C. D.
5-Minute Check 5

12. A. B. C. D.
5-Minute Check 5

13. Mathematical Practices 4 Model with mathematics.
Content Standards
A.SSE.2 Use the structure of an expression to identify ways to rewrite it.
A.CED.1 Create equations and inequalities in one variable and use them to solve problems.
Mathematical Practices
4 Model with mathematics.
CCSS

14. You evaluated logarithmic expressions.
Solve logarithmic equations.
Solve logarithmic inequalities.
Then/Now

15. logarithmic inequality
logarithmic equation
logarithmic inequality
Vocabulary

16. Definition of logarithm
Solve a Logarithmic Equation
Solve
Original equation
Definition of logarithm
8 = 23
Power of a Power
Answer:
Example 1

17. Definition of logarithm
Solve a Logarithmic Equation
Solve
Original equation
Definition of logarithm
8 = 23
Power of a Power
Answer: x = 16
Example 1

18. Solve A.
B. n = 3
C. n = 9 D.
n =
Example 1

19. Solve A.
B. n = 3
C. n = 9 D.
n =
Example 1

20. Concept

21. You need to find x for the logarithmic equation.
Solve a Logarithmic Equation
Solve log4 x 2 = log4 (–6x – 8).
A B C. –4, – D. no solutions
Read the Test Item
You need to find x for the logarithmic equation.
Solve the Test Item
log4 x 2 = log4 (–6x – 8) Original equation
x 2 = (–6x – 8) Property of Equality for Logarithmic Functions
Example 2

22. x 2 + 6x + 8 = 0 Subtract (–6x – 8) from each side.
Solve a Logarithmic Equation
x 2 + 6x + 8 = 0 Subtract (–6x – 8) from each side.
(x + 4)(x + 2) = 0 Factor.
x + 4 = 0 or x + 2 = 0 Zero Product Property
x = – x = –2 Solve each equation.
Example 2

23. Substitute each value into the original equation.
Solve a Logarithmic Equation
Check
Substitute each value into the original equation.
x = –4 ?
log4 (–4)2 = log4 [–6(–4) – 8)]
log4 16 = log4 16 
x = –2 ?
log4 (–2)2 = log4 [–6(–2) – 8)]
log4 4 = log4 4 
Answer:
Example 2

24. Substitute each value into the original equation.
Solve a Logarithmic Equation
Check
Substitute each value into the original equation.
x = –4 ?
log4 (–4)2 = log4 [–6(–4) – 8)]
log4 16 = log4 16 
x = –2 ?
log4 (–2)2 = log4 [–6(–2) – 8)]
log4 4 = log4 4 
Answer: The solutions are x = –4 and x = –2. The answer is C.
Example 2

25. Solve log4 x 2 = log4 (x + 20). A. 5 and –4 B. –2 and 10 C. 2 and –10
D. no solutions
Example 2

26. Solve log4 x 2 = log4 (x + 20). A. 5 and –4 B. –2 and 10 C. 2 and –10
D. no solutions
Example 2

27. Concept

28. log6 x > 3 Original inequality
Solve a Logarithmic Inequality
Solve log6 x > 3.
log6 x > 3 Original inequality
x > 63 Property of Inequality for Logarithmic Functions
x > 216 Simplify.
Answer:
Example 3

29. log6 x > 3 Original inequality
Solve a Logarithmic Inequality
Solve log6 x > 3.
log6 x > 3 Original inequality
x > 63 Property of Inequality for Logarithmic Functions
x > 216 Simplify.
Answer: The solution set is {x | x > 216}.
Example 3

30. What is the solution to log3 x < 2?
A. {x | x < 9}
B. {x | 0 < x < 9}
C. {x | x > 9}
D. {x | x < 8}
Example 3

31. What is the solution to log3 x < 2?
A. {x | x < 9}
B. {x | 0 < x < 9}
C. {x | x > 9}
D. {x | x < 8}
Example 3

32. Concept

33. Solve log7 (2x + 8) > log7 (x + 5).
Solve Inequalities with Logarithms on Each Side
Solve log7 (2x + 8) > log7 (x + 5).
log7 (2x + 8) > log7 (x + 5) Original inequality
2x + 8 > x + 5 Property of Inequality for Logarithmic Functions
x > –3 Simplify.
Answer:
Example 4

34. Solve log7 (2x + 8) > log7 (x + 5).
Solve Inequalities with Logarithms on Each Side
Solve log7 (2x + 8) > log7 (x + 5).
log7 (2x + 8) > log7 (x + 5) Original inequality
2x + 8 > x + 5 Property of Inequality for Logarithmic Functions
x > –3 Simplify.
Answer: The solution set is {x | x > –3}.
Example 4

35. Solve log7 (4x + 5) < log7 (5x + 1).A. B. C. D.
{x | x > 4}
{x | x ≥ 4}
{x | 0 < x < 4}
Example 4

36. Solve log7 (4x + 5) < log7 (5x + 1).A. B. C. D.
{x | x > 4}
{x | x ≥ 4}
{x | 0 < x < 4}
Example 4

37. End of the Lesson