1. Warm – up # 2 1. Rewrite in log form 5 4 =625 𝑙𝑜𝑔 5 625=4
2. Evaluate 𝑙𝑜𝑔 𝑥 128=7
𝑥 7 =128
𝑥 7 = 2 7
x = 2

2. Homework Log Tues 2/9 Lesson 7 – 4 Learning Objective:
To rewrite logs using properties of logs
Hw: Pg. 466 #9 – 37 odd

3. 2/9/16 Lesson 7 – 4 Properties of Logs Day 1
Algebra II

4. Learning Objective
To expand and condense logs using properties of logs

5. Properties of Logs
Product Property 𝑙𝑜𝑔 𝑏 𝑚𝑛= 𝑙𝑜𝑔 𝑏 𝑚+ 𝑙𝑜𝑔 𝑏 𝑛 Quotient Property 𝑙𝑜𝑔 𝑏 𝑚 𝑛 = 𝑙𝑜𝑔 𝑏 𝑚− 𝑙𝑜𝑔 𝑏 𝑛 Power Property 𝑙𝑜𝑔 𝑏 𝑚 𝑛 =𝑛 𝑙𝑜𝑔 𝑏 𝑚

6. Expand the logs
1. 𝑙𝑜𝑔 3 9 𝑥 5 𝑦 = 𝑙𝑜𝑔 3 9+ 𝑙𝑜𝑔 3 𝑥 5 + 𝑙𝑜𝑔 3 𝑦 = 𝑙𝑜𝑔 𝑙𝑜𝑔 3 𝑥+ 𝑙𝑜𝑔 3 𝑦 =2+ 5𝑙𝑜𝑔 3 𝑥+ 𝑙𝑜𝑔 3 𝑦 2. 𝑙𝑜𝑔 4𝑥 𝑦 = log 4x – log y = log 4 + log x – log y

7. Expand the logs
3. log ( 𝑚 2 𝑛 5 ) = log 𝑚 2 + log 𝑛 5 =2 log 𝑚 +5 log 𝑛 4. 𝑙𝑜𝑔 2 𝑥 = 𝑙𝑜𝑔 2 𝑥 1/2 = 1 2 𝑙𝑜𝑔 2 𝑥 or = 𝑙𝑜𝑔 2 𝑥 2

8. Expand the logs
5. 𝑙𝑜𝑔 4 𝑥 5 𝑦 7 𝑧 𝑤 4 = 𝑙𝑜𝑔 4 ( 𝑥 5 𝑦 7 ) 1/2 𝑧 𝑤 4 = 𝑙𝑜𝑔 4 𝑥 5/2 𝑦 7/2 𝑧 𝑤 4 = 𝑙𝑜𝑔 4 ( 𝑥 5/2 𝑦 7/2 )− 𝑙𝑜𝑔 4 (𝑧 𝑤 4 ) = 𝑙𝑜𝑔 4 𝑥 𝑙𝑜𝑔 4 𝑦 7 2 − 𝑙𝑜𝑔 4 𝑧− 𝑙𝑜𝑔 4 𝑤 4 = 5 2 𝑙𝑜𝑔 4 𝑥+ 7 2 𝑙𝑜𝑔 4 𝑦− 𝑙𝑜𝑔 4 𝑧−4 𝑙𝑜𝑔 4 𝑤

9. Expand the logs
6. 𝑙𝑜𝑔 4𝑥 𝑦 −3 𝑤 4 = 𝑙𝑜𝑔 ( 4𝑥 𝑦 −3 𝑤 4 ) 1/2 = 𝑙𝑜𝑔 4 1/2 𝑥 1/2 𝑦 −3/2 𝑤 2 = 𝑙𝑜𝑔( 4 1/2 𝑥 1/2 )−𝑙𝑜𝑔( 𝑦 −3/2 𝑤 2 ) = 𝑙𝑜𝑔2+𝑙𝑜𝑔 𝑥 1 2 −𝑙𝑜𝑔 𝑦 −3/2 −𝑙𝑜𝑔 𝑤 2 = 𝑙𝑜𝑔 𝑙𝑜𝑔𝑥+ 3 2 𝑙𝑜𝑔𝑦−2𝑙𝑜𝑔𝑤

10. Condense/Write as a single log
7. 6 𝑙𝑜𝑔 5 𝑥+5 𝑙𝑜𝑔 5 𝑦− 𝑙𝑜𝑔 5 𝑧 = 𝑙𝑜𝑔 5 𝑥 6 + 𝑙𝑜𝑔 5 𝑦 5 − 𝑙𝑜𝑔 5 𝑧 = 𝑙𝑜𝑔 5 ( 𝑥 6 𝑦 5 𝑧 ) NOT 𝑙𝑜𝑔 5 ( 𝑥 6 + 𝑦 5 𝑧 ) NOT 𝑙𝑜𝑔 5 (𝑥 6 𝑦 5 ) 𝑙𝑜𝑔 5 𝑧 NOT 𝑙𝑜𝑔 5 (𝑥 6 𝑦 5 ) 𝑧

11. Condense/Write as a single log
8. 3 𝑙𝑜𝑔 2 𝑥+ 𝑙𝑜𝑔 2 5−2 𝑙𝑜𝑔 2 𝑧− 𝑙𝑜𝑔 2 7 = 𝑙𝑜𝑔 2 𝑥 3 + 𝑙𝑜𝑔 2 5− 𝑙𝑜𝑔 2 𝑧 2 − 𝑙𝑜𝑔 2 7 = 𝑙𝑜𝑔 2 ( 5 𝑥 3 7 𝑧 2 ) NOT 𝑙𝑜𝑔 2 ( 5+ 𝑥 3 𝑧 2 −7 ) NOT 𝑙𝑜𝑔 2 (5𝑥 3 ) 𝑙𝑜𝑔 2 (7 𝑧 2 ) NOT 𝑙𝑜𝑔 1 (5𝑥 2 ) 7 𝑧 2

12. Condense/Write as a single log
9. 2 𝑙𝑜𝑔 𝑏 𝑥 𝑙𝑜𝑔 𝑏 𝑦 4 −5 𝑙𝑜𝑔 𝑏 𝑧 = 𝑙𝑜𝑔 𝑏 𝑥 2/3 + 𝑙𝑜𝑔 𝑏 𝑦 3/4 − 𝑙𝑜𝑔 𝑏 𝑧 5 = 𝑙𝑜𝑔 𝑏 𝑥 2/3 𝑦 3/4 𝑧 5 Or = 𝑙𝑜𝑔 𝑏 3 𝑥 2 ∙ 4 𝑦 3 𝑧 5

13. Condense/Write as a single log
10. 𝑙𝑜𝑔 4 32− 𝑙𝑜𝑔 4 2 = 𝑙𝑜𝑔 = 𝑙𝑜𝑔 𝑥 =16 = 2
11. 𝑙𝑜𝑔 6 24− 𝑙𝑜𝑔 6 4
= 𝑙𝑜𝑔
= 𝑙𝑜𝑔 6 6
6 𝑥 =6
= 1

14. Condense/Write as a single log
12. 𝑙𝑜𝑔 𝑙𝑜𝑔 64 8 = 𝑙𝑜𝑔 64 (2∙8) = 𝑙𝑜𝑔 𝑥 =16 ( 2 6 ) 𝑥 = 𝑥 = 2 4 6x = 4 𝑥= 2 3

15. Ticket Out the Door Condense into one log
1 2 𝑙𝑜𝑔 𝑥 4+ 𝑙𝑜𝑔 𝑥 𝑦 −3 𝑙𝑜𝑔 𝑥 𝑧
Check your work by expanding your answer

16. Assignment: Pg. 466 #9 – 37 odd

17. Extra Credit for Winners!
BINGO
Extra Credit for Winners!

18. Rewrite in Log Form

19. Solve for x.

20. Evaluate

21. Evaluate

22. Rewrite in Exponential Form.

23. Rewrite in Log Form

24. Evaluate

25. Evaluate

26. Evaluate

27. Evaluate

29. Evaluate

30. Rewrite in Log Form

31. Evaluate

32. Evaluate

33. Solve for n.

34. Rewrite in Exponential Form.

35. Rewrite in Log Form

36. Evaluate

37. Solve for x

38. Rewrite in Exponential Form.

39. Solve for a.

40. Rewrite in Exponential Form

41. Solve for m.

42. Evaluate

43. Evaluate

44. Rewrite in Exponential Form

45. Evaluate

46. Rewrite in Log Form

47. Solve for x.

48. Rewrite in Log Form

49. Solve for x.

50. Rewrite in Exponential Form.

51. Rewrite in Log Form

52. Solve for x

53. Rewrite in Exponential Form.