1. Properties of Logarithmic Functions
Demana, Waits, Foley, Kennedy
3.4
Properties of Logarithmic Functions

2. What you’ll learn about
Properties of Logarithms
Change of Base
Graphs of Logarithmic Functions with Base b
Re-expressing Data
… and why
The applications of logarithms are based on their many
special properties, so learn them well.

3. Adding Logarithms
Evaluate and rewrite as a single log expression log10 + log100 = _______ = log( )
log10 + log1000 =_______ = log( )
log10 + log10 = _______ = log( )
logA + logB = log( )
Why does this work?

4. Subtracting Logarithms
Evaluate and rewrite as a single log expression log log10 = _______ = log( )
log100 - log10 =_______ = log( )
log10 – log.01 = _______ = log( )
logA - logB = log( )
Why does this work?

5. Logarithms with exponents

6. Properties of Logarithms

7. Example: Proving the Product Rule for Logarithms

8. Solution

9. Example: Expanding the Logarithm of a Product

10. Solution

11. Example: Condensing a Logarithmic Expression

12. Solution

13. Example: Evaluating Logarithms by Changing the Base

14. Solution

15. Change-of-Base Formula for Logarithms

16. Example: Transforming Logarithmic Graphs

17. Solution

18. Solution

19. Solution