1. 5.5 Objectives Apply the base properties of logarithms. Use the change of base formula.

2. Properties of Logarithms 1)log a 1=0 and log a a=1 2)log a m+log a n=log a (mn) 3)log a m-log a n=log a (m/n) 4)log a (m r )=rlog a m ln = log e (natural log)

3. Change of base formula Let x, a, and b be positive numbers....where a≠ 1 and b≠ 1.

4. Try these ln 5+ ln 4log 10-log 5

5. And more… log 5 2 log 5 + log 15 – log 10

7. 5.6 Objectives Solve exponential equations Solve logarithmic equations.

8. Exponential Equations Basic form: Ca x = k 1)Solve for a x 2)take the base a log of both sides, which makes the a x equal x because.. log a a x = x 3)Solve the other side

10. Try these Log (2x+1) =2

11. Try these Log 2 4x = 2-log 2 x

12. Logarithmic equations Basic form: C log a x = k. 1)Solve for log a x. 2)Exponentiate each side with base a. This makes the log a x side equal x because a log a x = x 1)Solve.

13. Try these log x + log (2x+1) = log 72log 2 3x= 1

14. 5.7 Objectives Find an exponential model. Find a logarithmic model.

15. Types of models Exponential – f(x) = Ca x – Can be used to model data that increase or decrease rapidly over time Logarithmic – f(x) = a + b log x – Can be used to model data that increase gradually over time Logistic – f(x) = – Can be used to model data that at first increase slowly, then increase rapidly, and finally level of

16. Exponential model f(x) = Ca x

17. Logarithmic model f(x) = a + b log x

18. Logistic model

19. assignment Page 442-443 – 7-14 – 31-38 Page 453 – 5-14 – 33-38 Page 462 – 1-4