2. Section 7-5 Properties of Logarithms

3. Objectives I can evaluate Common Logs using a calculator I can use Change Base Rule I can expand log expressions using log properties I can condense log expressions using properties

4. Common Logarithms Your calculator has a button in the 7 th row called LOG. This button will calculate the base 10 common logarithm of a number. Example: log 125 = 2.097 ROUND to 3 decimal places

5. Examples log 135 = 2.130

6. Change of Base Formula

7. Find: log 8 77.

8. Find: log 16 64.

9. 3 Main Properties Product Property Quotient Property Power Property

10. Product Property log b mn = log b m + log b 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)

11. Product Rule log 2 4x = log 2 4 + log 2 x This is called expanding a log expression

12. Working Backwards log 3 x + log 3 3 + log 3 9 log 3 3x + log 3 9 log 3 27x This is called condensing an expression

13. Quotient Property log b m/n = log b m – log b n Left to Right (Expanding) Right to Left (Condensing)

14. Quotient Rule This is Expanding

15. Working Backwards log 3 x - log 3 3 log 3 x/3 This is called condensing an expression

16. Power Property log b m p = p log b m Left to Right (Expanding) Right to Left (Condensing)

17. Power Rule log 2 x 3 = 3log 2 x This is Expanding

18. Conversions

19. Condensing

21. Homework Worksheet 11-4