1. 6/4/2016 6:09 PM7.4 - Properties of Logarithms Honors1 Properties of Logarithms Section 7.4

2. 6/4/2016 6:09 PM7.4 - Properties of Logarithms Honors2 Review Product: Quotient: Power: n + m n – m n* m

3. 6/4/2016 6:09 PM7.4 - Properties of Logarithms Honors3 Review Review: What’s and Answer: 8 and 16 because its 2 · 2 · 2 = 8 and 2 · 2 · 2 · 2 = 16. So we know that and. However, what’s We’ll answer that question later…

4. Exponential and logarithmic operations undo each other since they are inverse operations.

5. Example 1: Recognizing Inverses Simplify each expression. b. log 3 81c. 5 log 5 10 a. log 3 3 11 log 3 3 11 11 log 3 3 4 4 5 log 5 10 10

6. b. Simplify 2 log 2 (8x) a. Simplify log10 0.9 0.9 8x8x Example 2 log 10 0.9 2 log 2 (8x)

7. 6/4/2016 6:09 PM7.4 - Properties of Logarithms Honors7 Properties of Logarithms Product: Quotient: Power:

8. Express log 6 4 + log 6 9 as a single logarithm. Simplify. Example 3: Adding Logarithms log 6 4 + log 6 9 log 6 (4  9) log 6 36 2

9. 6/4/2016 6:09 PM9 Example 4 Simplify as a single logarithm. What is the operation shown in this problem? MULTIPLY/PRODUCT

10. 6/4/2016 6:09 PM7.4 - Properties of Logarithms Honors10 Example 5 simplify as a single logarithm. What is the operation shown in this problem? MULTIPLY/PRODUCT

11. 6/4/2016 6:09 PM Example 6 Simplify as a single logarithm. What is the operation shown in this problem? DIVIDE/QUOTIENT

12. 6/4/2016 6:09 PM7.4 - Properties of Logarithms Honors12 Example 7 Simplify as a single logarithm. What is the operation shown in this problem? DIVIDE/QUOTIENT

13. Express as a single logarithm. Simplify, if possible. Example 8 2

14. Express as a single logarithm. Simplify, if possible. 1 Example 9

15. 6/4/2016 6:09 PM7.4 - Properties of Logarithms Honors15 Example 10 simplify as a single logarithm. What is the operation shown in this problem? POWER PROPERTY

16. 6/4/2016 6:09 PM7.4 - Properties of Logarithms Honors16 Example 11 Simplify as a single logarithm. What is the operation shown in this problem? POWER PROPERTY

17. 6/4/2016 6:09 PM7.4 - Properties of Logarithms Honors17 Example 12 simplify as a single logarithm.

18. 6/4/2016 6:09 PM7.4 - Properties of Logarithms Honors18 Example 13 Solve for x,

19. 6/4/2016 6:09 PM7.4 - Properties of Logarithms Honors19 Example 14 Solve for x,

20. 6/4/2016 6:09 PM7.4 - Properties of Logarithms Honors20 Example 15 simplify as a single logarithm.

21. 6/4/2016 6:09 PM7.4 - Properties of Logarithms Honors21 Example16 simplify

22. 6/4/2016 6:09 PM7.4 - Properties of Logarithms Honors22 Your Turn 1.Simplify: 2.Simplify: 3.Simplify: 4.Simplify:

23. 6/4/2016 6:09 PM7.4 - Properties of Logarithms Honors23 Example 12 The Richter magnitude of an earthquake, M, is related to the energy released in ergs, E, by the formula.. Find the energy released by an earthquake of magnitude 4.2.

24. 6/4/2016 6:09 PM7.4 - Properties of Logarithms Honors24 Assignment Pg 516: 20-35 all, omit 34 20-31 use without a graphing calculator