1. Logarithms Rewrite the equations in exponential form.

2. More Logarithms Simplify the log without a calculator

3. Find the log button on your calculator USING THE CALCULATOR…

4. Taking Logs to the Axes Graph the function by completing the table. Pick values for x that are easy to evaluate. xf(x) Try graphing the base 10 function on your calculator:

5. More Properties of Logarithms Simplify the expression without a calculator

6. More Properties of Logarithms Simplify the expression without a calculator

7. More Properties of Logarithms Because Logarithms come from exponential expressions, they have similar properties.

8. More Properties of Logarithms Expand:

9. More Properties of Logarithms Expand:

10. More Properties of Logarithms Condense:

11. More Properties of Logarithms Condense:

12. More Properties of Logarithms

13. Solve for x…

15. Solving Equations Warm-up

16. Solving Equations

19. Applications: Sheep population Retro virus Zappa is decimating the sheep population in the Tungan wastelands. The sheep population is currently 300,000 and is shrinking at a rate of 7% per year a) Write a function V(t) that will output the number of sheep after t years. b) Use the function in part (a) to find the sheep population in 10 years. c) If the trend continues, in how many years from now will the population drop to below 50,000 sheep? ?

20. Applications: U.S. population ? The population of the United States is currently 310,000,000 people. The population is increasing at a rate of 2% per year. a) Write a function V(t) that will output the population total after t years. b) What will be the population of the U.S. in twenty years? c) If the rate of growth continued, about how long would it take for the population of the U.S. to reach one billion people?

21. Applications: Car Value Depreciation A car is purchased for $25,000. It depreciates at the rate of 16% per year. a) Write a function V(t) that will output the value of the car after t years. b) Use the function from part (a) to determine how long it will take for the car to be worth $2000.

22. Applications: Bank Accounts You deposit $800 at a bank that pays 4.8% annual interest, compounded monthly. a)Write a function V(t) that will output the account balance after t-years. b) Use your function from part (a) to determine what your account balance will be after 12 years. (Round to the nearest $0.01) c) How long will it take for you to double your money?