Warm-up

1. Warm-up • 1. Convert the following log & exponential equations • Log equationExponential Equation • Log2 16 = 4 ? • Log3 1= 0 ? • ? 52 = 25 • 2. Solve these log expressions: • Log264 log99 log3(1/9) • 3. Graph this function: f(x) = log3(x – 2)

2. Warm-up • 1. Convert the following log & exponential equations • Log equationExponential Equation • Log2 16 = 4 • Log3 1 = 0 • ? 52 = 25

3. Warm-up • 2. Solve these log expressions: • Log264 • log99 • log3(1/9)

5. Property of Exponential Equality • xm = xn ; if and only if m = n • You will use this property a lot when trying to simplify.

6. Example 1: Solve • 64 = 23n+1 • We want the same base (2). Can we write 64 as 2? • 64 = 2x2x2x2x2x2 = 26 • 26 = 23n+1 • 6 = 3n + 1 • 3n = 5 • n = 5/3

7. Example 2: Solve • 5n-3 = 1/25 • We want the same base (5). Can we write 1/25 as 5? • 25 = 5x5 = 52 • 1/25 = 1/52 = 5-2 • 5n-3 = 5-2 • n – 3 = -2 • n = 1

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

9. Objectives • I can solve equations involving log properties

10. 3 Main Properties • Product Property • Quotient Property • Power Property

11. Product Property of Logarithms

12. Example Working Backwards • Solve the following for “x” • log4 2 + log4 6 = log4 x • log4 2•6 = log4 x • 2•6 = x • x = 12

13. Product Property

14. Quotient Property of Logs

15. Working Backwards • Log3 6 - Log3 12 • Log3 6/12 • Log3 1/2 • Condensing an expression

16. Quotient Property

17. Quotient Property Backwards • Solve the following for x • log5 42 – log5 6 = log5 x • log5 42/6 = log5 x • x = 42/6 • x = 7

18. Power Property of Logs

19. Example Power Property • 4 log5 x = log5 16 • log5 x4 = log5 16 • x4 = 16 • x4 = 24 • x = 2

20. Power Property

21. Practice

22. Practice

23. Practice

24. Practice

25. Practice

26. Practice

27. Practice

28. Homework • WS 6-3