1. Splash Screen

2. https://www. youtube. com/watch

3. Five-Minute Check (over Lesson 3-2) Then/Now
Key Concept: Properties of Logarithms
Example 1: Use the Properties of Logarithms
Example 2: Simplify Logarithms
Example 3: Expand Logarithmic Expressions
Example 4: Condense Logarithmic Expressions
Key Concept: Change of Base Formula
Example 5: Use the Change of Base Formula
Example 6: Use the Change of Base Formula
Lesson Menu

4. Evaluate A. B.
C. 1
D. 2
5–Minute Check 1

5. Evaluate log5 5.
A. –1
B. 0
C. 1
D. 5
5–Minute Check 2

6. Evaluate 10log 2.
A. 1
B. 2
C. 5
D. 10
5–Minute Check 3

7. Evaluate ln(–3). A. about –1.1 B. about 0.48 C. about 1.1 D. undefined
5–Minute Check 4

8. A. Sketch the graph of f (x) = log3 x.B. C. D.
5–Minute Check 5

9. B. Analyze the graph of f (x) = log3 x
B. Analyze the graph of f (x) = log3 x. Describe its domain, range, intercepts, asymptotes, end behavior, and where the function is increasing or decreasing.
A. D: (–∞, ∞); R: (0, ∞); x-intercept: 1; Asymptote: x-axis; Increasing (–∞, ∞) ;
B. D: (–∞, ∞); R: (0, ∞); x-intercept: 1; Asymptote: x-axis; Decreasing (–∞, ∞);
C. D: (0, ∞); R: (–∞, ∞); x-intercept: 1; Asymptote: y-axis; Increasing (0, ∞);
D. D: (0, ∞); R: (–∞, ∞); x-intercept: 1; Asymptote: y-axis; Decreasing (–∞, ∞);
5–Minute Check 5

10. Evaluate eIn x.
A. x
B. ln e
C. e
D. ex
5–Minute Check 6

11. Apply properties of logarithms. Apply the Change of Base Formula.
You evaluated logarithmic expressions with different bases. (Lesson 3–2)
Apply properties of logarithms.
Apply the Change of Base Formula.
Then/Now

12. Key Concept 1

13. A. Express: log 96 in terms of log 2 and log 3
Use the Properties of Logarithms
A. Express: log 96 in terms of log 2 and log 3
log 96 = log (25 ● 3) 96 = 25 ● 3
= log 25 + log 3 Product Property
= 5 log 2 + log 3 Power Property
Answer: 5 log 2 + log 3
Example 1

14. B. Express: in terms of log 2 and log 3
Use the Properties of Logarithms
B. Express: in terms of log 2 and log 3
= log 32 – log 9 Quotient Property
= log 25 – log32 25 = 32 and 32 = 9
= 5 log 2 – 2 log 3 Power Property
Answer: 5 log 2 – 2 log 3
Example 1

15. Express: ln in terms of ln 3 and ln 5
A. 3 ln ln 3
B. ln 53 – ln 33
C. 3 ln 5 – 3 ln 3
D. 3 ln 3 – 3 ln 5
Example 1

16. Rewrite using rational exponents.
Simplify Logarithms
A. Evaluate
Rewrite using rational exponents.
25 = 32
Power Property of Exponents
Power Property of Logarithms
logx x = 1
Answer:
Example 2

17. 3 ln e4 – 2 ln e2 = 4(3 ln e) – 2(2 ln e) Power Property of Logarithms
Simplify Logarithms
B. Evaluate: ln e4 – 2 ln e2
3 ln e4 – 2 ln e2 = 4(3 ln e) – 2(2 ln e) Power Property of Logarithms
= 12 ln e – 4 ln e Multiply.
= 12(1) – 4(1) or 8 ln e = 1
Answer: 8
Example 2

18. Evaluate:
A. 4 B. C. D.
Example 2

19. The expression is the logarithm of the product of 4, m3, and n5.
Expand Logarithmic Expressions
A. Expand ln 4m3n5.
The expression is the logarithm of the product of 4, m3, and n5.
ln 4m3n5 = ln 4 + ln m3 + ln n5 Product Property
= ln ln m + 5 ln n Power Property
Answer: ln ln m + 5 ln n
Example 3

20. The expression is the logarithm of the quotient of 2x – 3 and
Expand Logarithmic Expressions
B. Expand
The expression is the logarithm of the quotient of 2x – 3 and
Quotient Property
Product Property
Rewrite using rational exponents.
Power Property
Example 3

21. Expand Logarithmic Expressions
Answer:
Example 3

22. Expand A. 3 ln x – ln (x – 7) B. 3 ln x + ln (x – 7)
C. ln (x – 7) – 3 ln x
D. ln x3 – ln (x – 7)
Example 3

23. A. Condense . Power Property Quotient Property Answer:
Condense Logarithmic Expressions
A. Condense
Power Property
Quotient Property
Answer:
Example 4

24. B. Condense: 5 ln (x + 1) + 6 ln x
Condense Logarithmic Expressions
B. Condense: ln (x + 1) + 6 ln x
5 ln (x + 1) + 6 ln x = ln (x + 1)5 + ln x6 Power Property
= ln x6(x + 1)5 Product Property
Answer: ln x6(x + 1)5
Example 4

25. Condense: – ln x2 + ln (x + 3) + ln x
A. In x(x + 3) B. C. D.
Example 4

26. Key Concept 2

27. log 6 4 = Change of Base Formula
Use the Change of Base Formula
A. Evaluate: log 6 4
log 6 4 = Change of Base Formula
≈ 0.77 Use a calculator.
Answer: 0.77
Example 5

28. = Change of Base Formula
Use the Change of Base Formula
B. Evaluate
= Change of Base Formula
≈ –1.89 Use a calculator.
Answer: –1.89
Example 5

29. Evaluate
A. –2
B. –0.5
C. 0.5
D. 2
Example 5

30. End of the Lesson