Lesson 3.1-3.3 Review - Miami-Dade County Public Schools

Lesson 3.1-3.3 Review

Name___________________________________

Period

Date

Directions: Do all work on a seperate sheet of paper and place all answers in the answer column provided. SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Graph the function by making a table of coordinates.

1) f(x) = 2x

1)

y 6

4

2

-6 -4 -2 -2 -4 -6

2 4 6x

2) f(x) =

5x 4

2)

y 6

4

2

-6 -4 -2 -2 -4 -6

2 4 6x

Graph the function.

3) Use the graph of f(x) = 2x to obtain the graph of g(x) = 2x - 1.

3)

y 6 4 2

-6 -4 -2 -2 -4 -6

2 4 6x

1

4) Use the graph of f(x) = 4x to obtain the graph of g(x) = 4x + 1 - 1.

4)

y 6 4 2

-6 -4 -2 -2 -4 -6

2 4 6x

5) Use the graph of f(x) = 3x to obtain the graph of g(x) = 3 ? 3x.

5)

y 6

4

2

-6 -4 -2 -2

-4

-6

2 4 6x

Use the compound interest formulas to solve. 6) Find the accumulated value of an investment of $ 17,000 at 6% compounded annually for 13 6) years.

7) Find the accumulated value of an investment of $ 900 at 12% compounded quarterly for 2

7)

years.

8) Suppose that you have $4000 to invest. Which investment yields the greater return over 6

8)

years: 7.2% compounded monthly or 7.3% compounded quarterly?

Write the equation in its equivalent exponential form.

9) log b 9 = 2

9)

10) log 2 16 = x

10)

Write the equation in its equivalent logarithmic form.

11)

2-3

=

1 8

11)

12) 3 125 = 5

12)

2

Evaluate the expression without using a calculator.

13) log 3 27

13)

14) log 10 10

14)

15)

log 5

1 25

15)

16) 7 log 7 20

16)

17) log 4 4

17)

Graph the function.

18) Use the graph of log 5 x to obtain the graph of f(x) = log 5 (x - 1).

18)

y

10

5

-10

-5

-5

-10

5

10 x

19) Use the graph of log 2 x to obtain the graph of f(x) = 2 log 2 x.

19)

y

10

5

-10

-5

-5

-10

5

10 x

3

20) Use the graph of f(x) = log x to obtain the graph of g(x) = log (x + 5).

20)

y 10

5

-10

-5

-5

-10

5

10 x

Find the domain of the logarithmic function.

21) f(x) = log 7 (x - 8)

21)

22) f(x) = ln (8 - x)

22)

23) f(x) = log 5 (x - 4)2

23)

24) f(x) = log (x2 - 12x + 27)

24)

Evaluate or simplify the expression without using a calculator.

25) log

1 100

25)

26) log 1000

26)

27) 10log 3

27)

28) 10log 6 x

28)

29) ln e6

29)

30) ln e12

30)

31) ln e

31)

4

32) ln e

32)

Evaluate the expression without using a calculator.

33) eln 8x4

33)

4

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate

logarithmic expressions without using a calculator.

34) logb (yz6)

34)

35) logb (yz4)

35)

36) log 2

x - 2 x6

36)

6

37) ln ey

37)

38) log3

81 x - 1

38)

39) loga

x4 3 x + 5 (x -2)2

39)

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose

coefficient is 1. Where possible, evaluate logarithmic expressions.

40) 4 log b q - log b r

40)

41) log 5 (x - 3) - log 5 (x + 8)

41)

42) log1025 + log1040

42)

43) 4logby + 8logbz

43)

44)

1 2

(log5

(r - 4)

- log5

r)

44)

45)

1 6

(log6

x + log6

y) - 2 log6

(x +

3)

45)

Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places

46) log 19 81.1

46)

47) log 26

47)

48) log 29 353

48)

49) log 7 20

49)

50) log 0.8 20

50)

5

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