1. 2 Switching From Exp and Log Forms Solving Log Equations Properties of Logarithms Solving Exp Equations Growth and Decay Problems 100 200 300 400 500.

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Presentation transcript:

1

2 Switching From Exp and Log Forms Solving Log Equations Properties of Logarithms Solving Exp Equations Growth and Decay Problems

3 Switching From Exp and Log Forms 100 Switch 2 x = 16 to log form.

4 Switching From Exp and Log Forms 200 Switch 100 = 10 x to log form.

5 Switching From Exp and Log Forms 300 Switch log 5 25 = x to exponential form and solve for x.

6 Switching From Exp and Log Forms 400 Switch log = x to exponential form and solve for x.

7 Switching From Exp and Log Forms 500 Combine log 2 80 – log 2 5 = x into one logarithm, then switch to exponential form to solve.

8 Solving Log Equations 100 Solve the logarithmic equation

9 Solving Log Equations 200 Solve the logarithmic equation log – log 5 5 = x

10 Solving Log Equations 300 Solve the logarithmic equation

11 Solving Log Equations 400 Solve the logarithmic inequality. Write your solution in interval notation. (Hint: Don’t forget that you can only take the log of a positive number.)

12 Solving Log Equations 500 Solve the logarithmic inequality. Write your solution in interval notation.

13 Properties of Logarithms 100 Simplify the expression

14 Properties of Logarithms 200 Simplify the expression

15 Properties of Logarithms 300 Evaluate the following using a calculator and the change of base formula. Round to three decimal places. 1. log log 9 17

16 Properties of Logarithms 400 Express the following as a single logarithm and simplify, if possible. 1.log log log – log 6 10

17 Properties of Logarithms 500 A log table says that log 2 = and log 9 = Describe how to find log 18 and log 2 9 and compute both.

18 Solving Exponential Equations 100 Solve the exponential equation

19 Solving Exponential Equations 200 Solve the exponential equation

20 Solving Exponential Equations 300 Solve the exponential equation. Round to three decimal places.

21 Solving Exponential Equations 400 Solve the exponential inequality. Write your solution in interval notation.

22 Solving Exponential Equations 500 Solve the exponential equation. Round to three decimal places.

23 Growth and Decay Problems 100 Use the decay equation A(t) = P(1 – r) t to solve the problem. A city population, which was initially 40,000 has been dropping at a rate of 2% per year. Approximate what the population will be in 20 years.

24 Growth and Decay Problems 200 Use the growth equation A(t) = P(1 + r) t to solve the problem. Ann invests $1000 in an account that pays 6.25% interest each year. How long will it take for Ann to have $1800?

25 Growth and Decay Problems 300 Brooke invests $1500 in an account that has an annual interest rate of 3%, compounded monthly. Use the equation to find how much money Brooke has after 10 years.

26 Growth and Decay Problems 400 Clay invests $2000 in an account that earns 4.5% interest per year, compounded continuously. Use A(t) = Pe rt to estimate how long it will take for his account to reach $2500.

27 Growth and Decay Problems A paleontologist uncovers a fossil of a saber- toothed tiger in California. He analyzes the fossil and concludes that the specimen contains 13% of its original carbon-14. Carbon-14 has a half-life of 5730 years. Use carbon-14 dating to determine the age of the fossil.