Free Printable Assessment: Lesson 6-3 and 6-4

1.

log(x+6) = 1

a)

4

b)

4.222

c)

-5

d)

-9.550

2.

Evaluate.

log₂32=3x

a)

5/3

b)

3/5

c)

5

d)

3

3.

log_x1000=3

a)

1

b)

10

c)

30

d)

3

4.

log₂(x+3)=4

a)

16

b)

13

c)

3

d)

10

5.

Solve for x:
log_x25 = 2

a)

5

b)

-5

c)

1/5

d)

-1/5

6.

Convert log(x) = 5 to exponential form

a)

1⁵=x

b)

10^x=5

c)

x⁵=10

d)

10⁵=x

7.

Convert 6^(x+2)=216 to logarithmic form

a)

log₂₁₆(x+2)=6

b)

log₆(x+2)=216

c)

log₆(216)=x+2

d)

log_(x+2)(216)=6

8.

Solve for x.
log_x(64)=3

a)

x=8

b)

x=4

c)

x=3

d)

x=64

9.

Solve for x
5^x = 17

a)

x = log₁₇5

b)

x = log 5 + log 17

c)

x = log₅17

d)

x = (log 5)/(log 17)

10.

Write in exponential form.
log₂(¹/₈) = -3

a)

2^-3 = ¹/₈

b)

2^1/8= -3

c)

-3² = ¹/₈

d)

-3^1/8 = 2

11.

Evaluate the following logarithm:

log₄16

a)

1

b)

-2

c)

2

d)

¹/₂

12.

Evaluate the following logarithm:

log₅5

a)

1

b)

0

c)

-1

d)

¹/₂

13.

Evaluate the following logarithm:

log₃27

a)

3

b)

2

c)

-3

d)

¹/₃

14.

Rewrite in exponential form:
log (x) = ¼

a)

x^1/4 = 1

b)

1^x=¼

c)

10^1/4 = x

d)

10^x = ¼

15.

Rewrite in exponential form:
ln(2) = x

a)

2^x= 10

b)

10² = x

c)

e^x= 2

d)

e² = x

16.

What is the value of ln(e⁷)

a)

2.718...

b)

1

c)

7

d)

Does not exist

17.

Solve for x:

e^2x = 11

a)

x = (ln 11)/2

b)

x = 2log_e11

c)

x = 2e(log11)

d)

x = ln (11/2)

18.

log_x1000 = 3

a)

1

b)

10

c)

30

d)

3

19.

Solve for x:
4²^x+ 1 = 17

a)

x = 1

b)

x = -1

c)

x = 2

d)

x = -2

20.

Solve for x:

2^{3x - 1} = 32

a)

0

b)

-1

c)

5/3

d)

2

21.

Solve: 7^-x = 49

a)

x = 1

b)

x = -1

c)

x = 2

d)

x = -2

22.

Logarithms and Exponentials are _______________?

a)

parallel

b)

perpendiular

c)

inverses

d)

congurent

23.

Rewrite log_vn = a in exponential form.

a)

v^a = n

b)

n^a = v

c)

vⁿ = a

d)

aⁿ = v

24.

Rewrite log_pt = m in exponential form.

a)

p^t = m

b)

t^m = p

c)

m^t = p

d)

p^m = t

25.

Solve for x.
5^x = 1

a)

0

b)

-1

c)

2

d)

1

26.

The common logarithm has what base?

a)

10

b)

0

c)

e

d)

-e

27.

Log with a base "e" (log_e) is the same thing as...

a)

"e"

b)

natural logarithm (ln)

c)

common logarithm (log)

d)

natural log, base "e" ln_e

28.

Change to Logarithmic Form:
5³ = 125

a)

log ₅ 125 = 3

b)

log₃125 = 5

c)

log ₅ 3 =125

d)

log₁₂₅ 3 = 5

29.

Solve for x:
4²^x+ 1 = 17

a)

x = 1

b)

x = -1

c)

x = 2

d)

x = -2

30.

log₈(1/2) = x

a)

-1/3

b)

1/3

c)

1/2

d)

-1/2

31.

log₆(2x + 3) = 3

a)

x = 106.5

b)

x = 100

c)

x = 16

d)

x = 50

32.

Solve for x.

log_x100 = 2

a)

10

b)

50

c)

10,000

d)

0.02

33.

a)

0.0005

b)

5.5

c)

121

d)

3.32

34.

a)

-2

b)

2

c)

4

d)

-4

35.

Solve for x.

log₆x = 3

a)

2

b)

729

c)

216

d)

18

36.

Solve for x.

log₃12 = x

a)

2.262

b)

0.442

c)

4

d)

1.401

37.

Evaluate the logarithmic expression without a calculator:

\log_{10}10,000

a)

1000

b)

4

c)

3

d)

5

38.

Evaluate the logarithmic expression without a calculator:

\log_{20}1

a)

0

b)

20

c)

1

d)

10

39.

The natural logarithm is represented as what?

a)

log

b)

ln

40.

The natural logarithm has what base?

a)

10

b)

0

c)

e

d)

-e

41.

Solve: 2^x = 25

Round to the nearest hundredth.

a)

x = 4.64

b)

x = 4.65

c)

x = 1.40

d)

x = 1.10

42.

Solve: 9^x-8 = 70

Round to the nearest hundredth.

a)

x = 9.93

b)

x = 1.93

c)

x = 1.85

d)

x = 9.85

43.

The base of common log is 10. So log 100 = ?

a)

1

b)

2

c)

10

d)

50

44.

Evaluate.

log1000

a)

1

b)

2

c)

3

d)

4

45.

Evaluate.

log 0.1

a)

-2

b)

-1

c)

1

d)

2

46.

Evaluate.

log 1

a)

-2

b)

-1

c)

0

d)

1

47.

Use a calculator to evaluate log 25

a)

1.398

b)

1.598

c)

-1.397

d)

0.80

48.

lnx = -3

a)

8.1548

b)

-8.1548

c)

0.0498

d)

-0.0498

49.

Evaluate.

log₅25

a)

2

b)

5

c)

25

d)

125

50.

Evaluate:
log₄16

a)

2

b)

4

c)

1/2

d)

-2

51.

Evaluate.

log₄1 =

a)

0

b)

1

c)

4

d)

Undefined

52.

Evaluate.
log₃81

a)

4

b)

¹/₄

c)

-4

d)

-¹/₄

53.

Evaluate.
log₆(¹/₂₁₆)

a)

3

b)

¹/₃

c)

-¹/₃

d)

-3

54.

Write in exponential form.
log₂32 = 5

a)

2^-5 = 32

b)

2³² = 5

c)

2⁵ = 32

d)

32⁵ = 2

55.

Write in exponential form.
log₂(¹/₈) = -3

a)

2^-3 = ¹/₈

b)

2^1/8= -3

c)

-3² = ¹/₈

d)

-3^1/8 = 2

56.

Write in logarithmic form.
5² = 25

a)

log₅2 = 25

b)

log₂25 = 5

c)

log₂₅5 = 2

d)

log₅25 = 2

57.

Write in logarithmic form.
2^-4 = ¹/₁₆

a)

log₂(¹/₁₆) = -4

b)

log_-4(¹/₁₆) = 2

c)

log_-4 2 = ¹/₁₆

d)

log₂(-4) = ¹/₁₆

58.

Rewrite log₂8 = 3 in exponential form

a)

2⁸ = 3

b)

2³ = 8

c)

3² = 8

d)

8³ = 2

59.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

60.

Rewrite e^x = 9 using a logarithm

a)

ln x = 9

b)

ln 9 = x

c)

log_x e = 9

d)

log₉ x = e

61.

Solve the equation for x.

a)

32

b)

25

c)

1.66

d)

512

62.

Solve

14^4-6x= 11

(round to the nearest tenth)

a)

5

b)

0.5

c)

0.1

d)

1

63.

What is the inverse of

c\left(x\right)=\log\left(x\right)

a)

$c^{-1}\left(x\right)=x^e$

b)

$c^{-1}\left(x\right)=\ln x$

c)

$c^{-1}\left(x\right)=x^{10}$

d)

$c^{-1}\left(x\right)=10^x$

64.

What is the inverse of

n\left(x\right)=\ln\left(x\right)

a)

$n^{-1}\left(x\right)=\log e$

b)

$n^{-1}\left(x\right)=x^e$

c)

$n^{-1}\left(x\right)=e^x$

d)

$n^{-1}\left(x\right)=x^{\ln}$

65.

Find the inverse of y=9^x

a)

y=log_x9

b)

y=log₁₀9

c)

x=log_y9

d)

y=log₉x

66.

Find the Inverse of $y\ =\ \log_4\left(x-1\right)$

a)

$y=x$

b)

$y=\log_34^x$

c)

$y=4^x+1$

d)

$y=4^{x+1}$

67.

Find the inverse of $y=\ln\left(x+3\right)$

a)

$y=e^x-3$

b)

$y=e^{x-3}$

c)

$y=e^x+3$

d)

$y=e^{x+3}$

68.

What are the inverse points for the coordinates:

(3, 0) , (2, -4), (5, 5) and (-6,8)

a)

(3,0) , (2, -4) , (5,5) , (6,8)

b)

(0,3) , (-4,2) , (5,5) , (8,-6)

c)

(3,2), (0, -4), (5, -6), (5,8)

69.

Find the inverse of $f(x)=10+7x$

a)

$f^{-1}(x)=\frac{x-7}{10}$

b)

$f^{-1}(x)=\frac{x-10}{7}$

c)

$f^{-1}(x)=\frac{1}{10+7x}$

70.

The inverse of the function f(x) is written as ...

a)

f ^-1(x)

b)

f ²(x)

c)

f '(x)

d)

f ⁺(x)

71.

Find the inverse of $f\left(x\right)=\frac{1}{4}x-7$

a)

f^-1(x) = 4x + 7

b)

f^-1(x) = -4x+28

c)

f^-1(x) = -4x - 7

d)

f^-1(x) = 4x+28

72.

Is the inverse function found correctly?

a)

yes

b)

no

73.

What does it mean to find the inverse of a function?

a)

the x's and y's are switched

b)

the x's and y's are divided by 2

c)

the x's and y's are made negative

d)

the x's and y's are the same

74.

What is the inverse of the points
(1,3)(2,4)(6,8)

a)

(3,1)(4,2)(8,6)

b)

(-3,-1)(-4,-2)(-8,-6)

c)

(1,3)(2,4)(6,8)

d)

(-1,-3)(-2,-4)(-6,-8)

75.

Find the inverse of y=9^x

a)

y=log_x9

b)

y=log₁₀9

c)

x=log_y9

d)

y=log₉x

Assessment: Lesson 6-3 and 6-4

Total questions: 75

Worksheet time: 6hrs 3mins

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