1. Happy Tuesday! Do the following:  Take out HW#3 HW #4:  P 722 #1, 4, 6-18 Update:  11.4 Quiz on Thursday/Friday  Unit 11 Test Thursday/ Friday April 30 th / May 1 st

2. Agenda Review HW #3 Presentations Logarithmic Functions Log War Closure

3. Review HW #3

4. Presentations

5. Presenting You will come up and talk about the credit cards that you found and their APR score. Which credit card do you prefer and why? Show your graph and talk about the interest that you accumulated over time. Make eye contact with the audience and speak in a loud voice. Be entertaining!

6. Reflection Take out a separate sheet of paper and answer the following questions: ① What was your take-away from this? ① When you look into credit cards, what are you going to look for now? ② Was this project useful for your future? Why or why not? ③ What can I change for next year?

7. Learning Objectives By the end of the period you will be able to: ① Evaluate expressions involving logarithms ② Write, evaluate, and graph logarithmic functions and inequalities. ③ Use properties to simplify logarithmic expressions

8. Intro How many times would you have to double $1 before you had $8? You could use an exponential equation to model this situation. 1(2) x = 8. You should be able to solve this equation by using mental math if you know 2 3 = 8. So you would have to double the dollar 3 times to have $8.

9. Intro How many times would you have to double $1 before you had $512? You could solve this problem if you could solve 2 x = 512 by using an inverse operation that undoes raising a base to an exponent equation to model this situation. This operation is called finding the logarithm!

10. 11.4 Logarithmic Functions Logarithm You can write an exponential equation as a logarithmic equation and vice versa. Read log b a= x, as “the log base b of a is x.” Notice that the log is the exponent. Reading Math

11. 11.4 Logarithmic Functions

12. Whiteboards! Write each logarithmic equation as an exponential equation. (a)log 2 512 = 9 (b) log 8 2 = ⅓ Write each exponential equation as a logarithmic equation. (c) 4 –2 = 1/16 (d) b 0 = 1

13. 11.4 Logarithmic Functions A logarithm with base 10 is called a common logarithm. If no base is written for a logarithm, the base is assumed to be 10. For example, log 5 = log 10 5.

14. Whiteboards! Evaluate the expression log 7 (1/49). **Hint** Try setting log 7 (1/49) = x

15. 11.4 Logarithmic Functions

16. Logarithm War Who has played the card game War? This is a two player game, so you will be partners with someone at your table. Every group will receive a deck of logarithm expressions. You will randomly split up the deck amongst both of you (each person should have 15). You can shuffle your cards in the beginning if you like, but once the game begins you must always take the first card in your deck and play it. The player with the highest evaluated expression takes all the cards played. If it is a tie, then you must deal W-A-R( 3 cards) and the 4 th card will be the determining factor of who gets that pile.

17. Logarithm War For example: MS. HULS’ card: log 3 (1/3) MS. SWENSON’S card: log 4 (16) Who would win?

18. 7.3 Logarithmic Functions Example 2: Evaluate without the use of a calculator. (a) log 5 125 (b) log 5 ⅕ (c) log 0.01

19. Whiteboards! log 7 (1/49)

20. Learning Objectives By the end of the period you will be able to: ① Evaluate expressions involving logarithms ② Write, evaluate, and graph logarithmic functions and inequalities. ③ Use properties to simplify logarithmic expressions

21. Because logarithms are exponents, you can derive the properties of logarithms from the properties of exponents

22. 11.4: Logarithmic Functions Remember that to multiply powers with the same base, you add exponents. What do you think you do when you multiply logs?

23. 11.4: Logarithmic Functions

24. The property in the previous slide can be used in reverse to write a sum of logarithms (exponents) as a single logarithm, which can often be simplified. Think: log j + log a + log m = log jam Helpful Hint

25. 11.4: Logarithmic Functions Remember that to divide powers with the same base, you subtract exponents What do you think you do when you divide logs?

26. 11.4: Logarithmic Functions Just as a 5 b 3 cannot be simplified, logarithms must have the same base to be simplified. Caution

27. 11.4: Logarithmic Functions Because you can multiply logarithms, you can also take powers of logarithms.

28. 11.4: Logarithmic Functions Equality Property

29. Example 3

30. Whiteboards!

31. 7.3 Logarithmic Functions Logarithmic Function Parent function is y = log 2 x. Since logarithms are the inverses of exponents, the inverse of an exponential function is the logarithmic function.

32. 7.3 Logarithmic Functions Example 4: y=log 3 (x+1) y<log 3 x -2

33. Interactive Quiz http://my.hrw.com/math06_07/nsmedia/practice_quizz es/alg2/alg2_pq_elf_03.html