1. College Algebra Chapter 4 Exponential and Logarithmic Functions
Section 4.4
Properties of Logarithms

2. 1. Apply the Product, Quotient, and Power Properties of Logarithms
2. Write a Logarithmic Expression in Expanded Form
3. Write a Logarithmic Expression as a Single Logarithm
4. Apply the Change-of-Base Formula

3. Apply the Product, Quotient, and Power Properties of Logarithms
Let b, x, and y be positive real numbers where b ≠ 1.
Product Property:
Quotient Property:
Power Property:
For these exercises, assume that all variable expressions represent positive real numbers.

4. Examples 1 – 3:
Use the product property of logarithms to write the logarithm as a sum. Then simplify if possible. 1. 2. 3.

6. Examples 4 – 6:
Use the quotient property of logarithms to write the logarithm as a difference. Then simplify if possible. 4. 5. 6.

8. Examples 7 – 9:
Apply the power property of logarithms. 7. 8. 9.

10. 1. Apply the Product, Quotient, and Power Properties of Logarithms
2. Write a Logarithmic Expression in Expanded Form
3. Write a Logarithmic Expression as a Single Logarithm
4. Apply the Change-of-Base Formula

11. Example 10:
Write the expression as the sum or difference of logarithms.

12. Example 11:
Write the expression as the sum or difference of logarithms.

13. Example 12:
Write the expression as the sum or difference of logarithms.

14. Example 13:
Write the expression as the sum or difference of logarithms.

15. Example 14:
Write the expression as the sum or difference of logarithms.

16. Example 15:
Write the expression as the sum or difference of logarithms.

18. 1. Apply the Product, Quotient, and Power Properties of Logarithms
2. Write a Logarithmic Expression in Expanded Form
3. Write a Logarithmic Expression as a Single Logarithm
4. Apply the Change-of-Base Formula

19. Example 16:
Write the logarithmic expression as a single logarithm with a coefficient of 1, and simplify as much as possible.

20. Example 17:
Write the logarithmic expression as a single logarithm with a coefficient of 1, and simplify as much as possible.

21. Example 18:
Write the logarithmic expression as a single logarithm with a coefficient of 1, and simplify as much as possible.

22. Example 19:
Write the logarithmic expression as a single logarithm with a coefficient of 1, and simplify as much as possible.

23. Example 20:
Write the logarithmic expression as a single logarithm with a coefficient of 1, and simplify as much as possible.

26. Examples 21 – 23:
Use
to approximate the value of
21.
22.
23.

28. 1. Apply the Product, Quotient, and Power Properties of Logarithms
2. Write a Logarithmic Expression in Expanded Form
3. Write a Logarithmic Expression as a Single Logarithm
4. Apply the Change-of-Base Formula

29. Apply the Change-of-Base Formula
Let a and b be positive real numbers such that a ≠ 1 and b ≠ 1. Then for any positive real number x
In particular,

30. Examples 24, 25:
Use the change-of-base formula and a calculator to approximate the logarithm to 4 decimal places.
24.
25.