Section 7-5

1. Section 7-5 Properties of Logarithms

2. 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

3. Common Logarithms • Your calculator has a button in the 7th 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

4. Examples • log 135 • = 2.130

5. Change of Base Formula

6. Find: log8 77 .

7. Find: log16 64 .

8. 3 Main Properties • Product Property • Quotient Property • Power Property

9. 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)

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

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

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

13. Quotient Rule This is Expanding

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

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

16. Power Rule • log2 x3 • = 3log2 x • This is Expanding

17. Conversions

18. Condensing

19. Condensing

20. Homework • Worksheet 11-4