1. Today in Pre-Calculus Go over homework Need a calculator Review Chapter 3 Homework

2. Converting to logs Example: 16 = 4 x Example: 17 = 3 x Example: 183 = e x

3. Converting to exponents Example: 3 = log 4 x Example: 4 = log 5 x Example: lnx = 2

4. Change of Base Formula Allows us to rewrite logs in terms of base 10 or e so we can calculate the value of the log. Example: Find the value log 4 28

5. Properties of Logs log10= lne= log10 x = lne x = log1=ln1= 10 logx =e lnx =

6. Condensing Log Expressions Example: condense: log 5 x - log 5 y Example: Condense: 3lnx + 4 ln(y+4)

7. Expanding Log Expressions Use the properties of logs to rewrite one log expression into multiple log terms. example: Expand log 8 12y

8. Solving exponential Equations

9. Solving Log Equations Example 1: log(4x + 2) – log(x – 1) = 1 Example 2: ln(x – 2) + ln(2x – 3) = 2lnx

10. Interest Compound interest: Continuously Compounded interest: A=Pe rt A: final amount P: principal r: interest rate k: number of payments per year t: number of years

11. Example How long will it take for an investment of $15,000 to grow to $27,000 if interest is compounded quarterly with a 7.5% interest rate? How long will it take if the interest is compounded continuously?

12. Graphs y = 2 x

13. Transformations y = 2 x+2

14. Transformations y = -2 x

15. Additional Practice Pg 286: 25-30all Pg 308: 17-23 odd Pg 317: 7-11odd, 15-21odd, 23-27odd Pg 331: 11-15odd Pg 341: 21-27odd Pg 345: 31,32,53,54