1. Factoring Warm-up

3. Properties of Logarithms
Section 7-5
Properties of Logarithms

4. Objectives I can expand log expressions using log properties
I can condense log expressions using properties

5. 3 Main Properties
Product Property
Quotient Property
Power Property

6. Product Property logb mn = logb m + logb n
You can use this property from left to right or from right back to the left.
Left to Right (Expanding)
Right to Left (Condensing)

7. Product Rule log2 4x = log2 4 + log2 x
This is called expanding a log expression

8. Working Backwards log3 x + log3 3 + log3 9 log3 3x + log3 9 log3 27x
This is called condensing an expression

9. Quotient Property logb m/n = logb m – logb n Left to Right (Expanding)
Right to Left (Condensing)

10. Quotient Rule
This is Expanding

11. Working Backwards log3 x - log3 3 log3 x/3
This is called condensing an expression

12. Power Property logb mp = p logb m Left to Right (Expanding)
Right to Left (Condensing)

13. Power Rule
log2 x3
= 3log2 x
This is Expanding

14. Conversions

15. BIG Picture Positive Logs (Numerator) Negative Logs (Denominator)
Don’t leave fractional exponents

16. Condensing

17. Condensing

18. Homework
Worksheet 11-8