2. Warm-up 1. Convert the following log & exponential equations 1. Convert the following log & exponential equations Log equationExponential Equation Log equationExponential Equation Log 2 16 = 4? Log 2 16 = 4? Log 3 1= 0? Log 3 1= 0? ?5 2 = 25 ?5 2 = 25 2. Solve these log expressions: 2. Solve these log expressions: Log 2 64log 9 9log 3 (1/9) Log 2 64log 9 9log 3 (1/9) 3. Graph this function: f(x) = log 3 (x – 2) 3. Graph this function: f(x) = log 3 (x – 2)

3. Warm-up 1. Convert the following log & exponential equations 1. Convert the following log & exponential equations Log equationExponential Equation Log equationExponential Equation Log 2 16 = 4 Log 2 16 = 4 Log 3 1 = 0 Log 3 1 = 0 ?5 2 = 25 ?5 2 = 25

4. Warm-up 2. Solve these log expressions: 2. Solve these log expressions: Log 2 64 Log 2 64 log 9 9 log 9 9 log 3 (1/9) log 3 (1/9)

6. Property of Exponential Equality x m = x n ; if and only if m = n x m = x n ; if and only if m = n You will use this property a lot when trying to simplify. You will use this property a lot when trying to simplify.

7. Example 1: Solve 64 = 2 3n+1 64 = 2 3n+1 We want the same base (2). Can we write 64 as 2 ? We want the same base (2). Can we write 64 as 2 ? 64 = 2x2x2x2x2x2 = 2 6 64 = 2x2x2x2x2x2 = 2 6 2 6 = 2 3n+1 2 6 = 2 3n+1 6 = 3n + 1 6 = 3n + 1 3n = 5 3n = 5 n = 5/3 n = 5/3

8. Example 2: Solve 5 n-3 = 1/25 5 n-3 = 1/25 We want the same base (5). Can we write 1/25 as 5 ? We want the same base (5). Can we write 1/25 as 5 ? 25 = 5x5 = 5 2 25 = 5x5 = 5 2 1/25 = 1/5 2 = 5 -2 1/25 = 1/5 2 = 5 -2 5 n-3 = 5 -2 5 n-3 = 5 -2 n – 3 = -2 n – 3 = -2 n = 1 n = 1

9. Using Log Properties to Solve Equations Section 3-3 Pg 239-245

10. Objectives I can solve equations involving log properties I can solve equations involving log properties

11. 3 Main Properties Product Property Product Property Quotient Property Quotient Property Power Property Power Property

12. Product Property of Logarithms

13. Example Working Backwards Solve the following for “x” Solve the following for “x” log 4 2 + log 4 6 = log 4 x log 4 2 + log 4 6 = log 4 x log 4 26 = log 4 x log 4 26 = log 4 x 26 = x 26 = x x = 12 x = 12

14. Product Property

15. Quotient Property of Logs

16. Working Backwards Log 3 6 - Log 3 12 Log 3 6 - Log 3 12 Log 3 6/12 Log 3 6/12 Log 3 1/2 Log 3 1/2 Condensing an expression Condensing an expression

17. Quotient Property

18. Quotient Property Backwards Solve the following for x Solve the following for x log 5 42 – log 5 6 = log 5 x log 5 42 – log 5 6 = log 5 x log 5 42/6 = log 5 x log 5 42/6 = log 5 x x = 42/6 x = 42/6 x = 7 x = 7

19. Power Property of Logs

20. Example Power Property 4 log 5 x = log 5 16 4 log 5 x = log 5 16 log 5 x 4 = log 5 16 log 5 x 4 = log 5 16 x 4 = 16 x 4 = 16 x 4 = 2 4 x 4 = 2 4 x = 2 x = 2

21. Power Property

22. Practice

23. Practice

24. Practice

25. Practice

26. Practice

27. Practice

28. Practice

29. Homework WS 6-3 WS 6-3