1

2

Switching From Exp and

Log Forms

Solving Log Equations

Properties of Logarithms

Solving Exp Equations

Growth and Decay

Problems

100 100 100 100 100

200 200 200 200 200

300 300 300 300 300

400 400 400 400 400

500 500 500 500 500

3

Switching From Exp and Log Forms100

• Switch 2x = 16 to log form.

4

Switching From Exp and Log Forms200

• Switch 100 = 10x to log form.

5

Switching From Exp and Log Forms 300

• Switch log525 = x to exponential form and solve for x.

6

Switching From Exp and Log Forms 400

• Switch log 100000 = x to exponential form and solve for x.

7

Switching From Exp and Log Forms 500

• Combine log280 – log25 = x into one logarithm, then switch to exponential form to solve.

8

Solving Log Equations100

• Solve the logarithmic equation

log5 (x + 4) =log5 (2x−8)

9

Solving Log Equations200

• Solve the logarithmic equation log5125 – log55 = x

10

Solving Log Equations300

• Solve the logarithmic equation 6log (2 1) 2x

11

Solving Log Equations400

• 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.) log

3(x −2) ≤4

12

Solving Log Equations500

• Solve the logarithmic inequality . Write your solution in interval notation. log

5(x −1)2 > 6

13

Properties of Logarithms100

• Simplify the expression 113log 3

14

Properties of Logarithms200

• Simplify the expression 5log 75

15

Properties of Logarithms300

• Evaluate the following using a calculator and the change of base formula. Round to three decimal places.1. log46

2. log917

16

Properties of Logarithms400

• Express the following as a single logarithm and simplify, if possible.

1.log1025 + log104

2.log6360 – log610

17

Properties of Logarithms500

• A log table says that log 2 = 0.3010300 and log 9 = 0.9542425. Describe how to find log 18 and log29 and compute both.

18

Solving Exponential Equations100

• Solve the exponential equation

109−x =100x+2

19

Solving Exponential Equations200

• Solve the exponential equation

43x−4 =8x−1

20

Solving Exponential Equations300

• Solve the exponential equation. Round to three decimal places.

53x−1 =10

21

Solving Exponential Equations400

• Solve the exponential inequality. Write your solution in interval notation.

4 x−3 ≤16

22

Solving Exponential Equations500

• Solve the exponential equation. Round to three decimal places.

5x−1 =3x+1

23

Growth and Decay Problems100

• 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.

( ) 1nt

rA t P

n

26

Growth and Decay Problems400

• Clay invests $2000 in an account that earns 4.5% interest per year, compounded continuously. Use A(t) = Pert to estimate how long it will take for his account to reach $2500.

27

Growth and Decay Problems 500

27

• 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.