1. Properties of Logarithmic Functions
Objective: Simplify and evaluate expressions involving logarithms.

5. Product and Quotient Properties of Logarithms
For
Product Property

6. Product and Quotient Properties of Logarithms
For
Product Property
Quotient Property

7. Product and Quotient Properties of Logarithms
For
Product Property
Quotient Property
You can use these properties to evaluate logarithmic expressions.

8. Example 1

9. Example 1

10. Example 1

11. Try This
Given that , approximate each expression.

12. Try This
Given that , approximate each expression.

13. Try This
Given that , approximate each expression.

14. Example 2

15. Example 2

16. Example 2

17. Try This
Write each expression as a single logarithm. Then, simplify if possible.

18. Try This
Write each expression as a single logarithm. Then, simplify if possible.

19. Try This
Write each expression as a single logarithm. Then, simplify if possible.

20. The Power Property of Logarithms
For , and any real number p:

21. Example 3

22. Example 3

23. Try This
Evaluate

24. Try This
Evaluate

25. Exponential-Logarithmic Inverse Properties
For b > 0 and :

26. Example 4

27. Example 4

28. Example 4

29. Try This
Evaluate each expression.

30. Try This
Evaluate each expression.

31. Try This
Evaluate each expression.

32. One-to-One Property of Logarithms
If , then x = y.

33. Example 5

34. Example 5

35. Example 5

37. Homework
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