Free Printable Alg 2 Ch. 6 Exponential & Logarithmic Functions

1.

Rewrite log_pt = m in exponential form.

a)

p^t = m

b)

t^m = p

c)

m^t = p

d)

p^m = t

2.

Change to Exponential Form:
log₆36 = 2

a)

2⁶=36

b)

6²=36

c)

36²=6

d)

36⁶=2

3.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

4.

ln(e^W)

a)

e

b)

W

c)

e^W

d)

undefined

5.

e^ln(f)

a)

f

b)

e

c)

e^f

d)

undefined

6.

log₅25 = ?

a)

2

b)

5

c)

125

d)

10

7.

Evaluate log₄1

a)

1

b)

0

c)

4

d)

undefined

8.

Evaluate log₅20 to the third decimal place

a)

0.537

b)

2.996

c)

1.301

d)

1.861

9.

log(A+B) = logA + logB

a)

True

b)

False

10.

(logA) / (logB) = logA - logB

a)

True

b)

False

11.

Expand

a)

6log₈v-2log₈u

b)

6log₈u-2log₈v

c)

3log₈u-2log₈v

d)

6log₈u+2log₈v

12.

Simplify

a)

A

b)

B

c)

C

d)

D

13.

Solve

a)

A

b)

B

c)

C

d)

D

14.

Courtney saved up $2,200 working as a waitress over the summer. She put this money into a bank account that earned 5.2% interest and is compounded daily. How much will she have in her account at the end of 4 years?

a)

$2201.25

b)

$2694.55

c)

$2707.45

d)

$2708.63

15.

Use multiple log properties to write as a single log:
3log₂x - log₂y + log₂z

a)

log₂(x/(yz))

b)

log₂(x³yz)

c)

log₂(x³z/y)

d)

log₂(x³/(yz))

16.

Expand completely: log(2x⁵)

a)

log 2 + 5log x

b)

5log 2 + 5log x

c)

5log 2 + log x

d)

log 10 + log x

17.

a)

F

b)

G

c)

H

d)

J

18.

Is this exponential growth or decay?

a)

Growth

b)

Decay

19.

What is the equation that represents the exponential function in the image below?

a)

y=3(½)^x

b)

y=3(2)^x

c)

y=(2)^x

d)

y=2(3)^x

20.

Write in logarithmic form.
5² = 25

a)

log₅2 = 25

b)

log₂25 = 5

c)

log₂₅5 = 2

d)

log₅25 = 2

21.

Write in exponential form.
log₂32 = 5

a)

2^-5 = 32

b)

2³² = 5

c)

2⁵ = 32

d)

32⁵ = 2

22.

Write log₂ 0.25 = -2 in exponential form

a)

-2²= 0.25

b)

-2^0.25= 2

c)

2^-2= 0.25

d)

No correct answer

23.

Write in logarithmic form.
5² = 25

a)

log₅2 = 25

b)

log₂25 = 5

c)

log₂₅5 = 2

d)

log₅25 = 2

24.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

25.

Evaluate.
log₃81

a)

4

b)

¹/₄

c)

-4

d)

-¹/₄

26.

Change to Exponential Form:
log₆36 = 2

a)

2⁶=36

b)

6²=36

c)

36²=6

d)

36⁶=2

27.

Evaluate:
log₄16

a)

2

b)

4

c)

1/2

d)

-2

28.

log₅25 = ?

a)

2

b)

5

c)

25

d)

125

29.

Evaluate log₅20 to the third decimal place

a)

0.537

b)

2.996

c)

1.301

d)

1.861

30.

Find the value for x to the third decimal place: 10^x =20

a)

2

b)

1.301

c)

0.5

d)

No Correct Answer

31.

log₄1 =

a)

0

b)

1

c)

4

d)

does not exist

32.

The graph represents _____________

a)

Exponential Growth

b)

Exponential Decay

c)

None

d)

a Line

33.

Compare the graph of f(x) = 3^x- 4 with the graph of f(x) = 3^x

a)

Graph shifted 4 units up

b)

Graph shifted 4 units down

c)

The graphs are the same

d)

Exponential Decay

34.

Is the graph linear, exponential or neither?

a)

Linear

b)

Exponential

c)

Neither

35.

Does the graph represent growth, decay, linear or none?

a)

Exponential Growth

b)

Exponential Decay

c)

Linear

d)

None

36.

What type of function is y = 3^x?

a)

Exponential Growth

b)

Exponential Decay

c)

Linear

d)

None of the above

37.

The table represents ...

a)

Linear function, Dividing by 2

b)

Exponential function, Growth, Adding by 50

c)

Exponential function, Decay, Dividing by 2

d)

Exponential function, Decay, Adding 50

38.

Evaluate the exponential function

f(x) = 3^x ; x = - 2

a)

f(-2) = - 81

b)

f(-2) = -9

c)

f(-2) = 1/9

d)

f(-2) = -1/81

39.

Evaluate

g(x) = 3(2)^x ; g(3) = ___

a)

g(3) = 216

b)

g(3) = 24

c)

g(3) = 18

d)

g(3) = 28

40.

y = 12^x

^{Evaluate x = 2}

a)

y = 1/144

b)

y = 1/24

c)

y = 144

d)

y = 24

41.

Which function is exponential?

a)

f(x)

b)

h(x)

c)

g(x)

42.

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

a)

y = 15(35)^x

b)

y = 15(1.35)^x

c)

y = 35(0.35)^x

d)

y = 35(1.15)^x

43.

What is the range of the function?

a)

(- 2, 5)

b)

$\left(0,\ \infty\right)$

c)

$\left(4,\ \infty\right)$

d)

$\left(-\infty,\infty\right)$

44.

Evaluate the exponential function when x = 0

Hint: PEMDAS

a)

f(0) = 3.7

b)

f(0) = 1

c)

f(0) = 0

d)

f(0) = 2.14

45.

What is the initial amount, for the function:

f(x) = 300(1.16)^x

a)

300

b)

1.16

c)

0.16

d)

3

e)

16%

46.

In Jack and the beanstalk, the beanstalk grows very rapidly. It began at a length of 3 ft and grew at a rate of 14% per minute

Write the exponential function for this example

a)

y=6(0.14)^x

b)

y=3(17)^x

c)

y=3(1.14)^x

d)

y=3(0.86)^x

e)

y=6(1.04)^x

47.

Write log_b(x/y) as two logs

a)

log_bx-log_by

b)

log_bx+log_by

c)

log_bx*log_by

d)

log_bx/log_by

48.

Solve the following for 'x';
log₆(3x - 2) = log₆(5x - 8)

a)

x = 3

b)

x = 2

c)

x = -1

d)

No Solution

49.

Find the inverse of f(x) = -4x - 12

a)

f^-1(x) = 4x - 3

b)

f^-1(x) = -1/4x - 3

c)

f^-1(x) = 1/4x + 3

d)

f^-1(x) = -4x - 3

50.

The inverse has been reflected over which line?

a)

y = -x

b)

y =x

c)

y = 0

d)

y = x + 1

51.

What is the domain and range of this graph?

a)

D: $\left(-\infty,\infty\right)$
R: $\left(-\infty,\infty\right)$

b)

D: $\left(-\infty,\infty\right)$
R: $\left[0,\ \infty\right)$

c)

D: $\left[2,\ \infty\right)$
R: $\left[3,\ \infty\right)$

d)

D: $\left(-\infty,2\right)$
R: $\left(-\infty,3\right)$

52.

Use multiple log properties to write as a sum or difference of two logs: log(4x³)

a)

log 4 + 3log x

b)

3log 4 + 3log x

c)

3log 4 + log x

d)

log 12 + log x

53.

Use multiple log properties to write as a single log:
log₂x - 5log₂y

a)

log₂(x/y⁵)

b)

log₂(xy⁵)

c)

log₂(x/y)⁵

d)

log₂(x/5y)

54.

Solve for x: log₆x + log₆(x-5) = 2

a)

x = √7

b)

x = 9

c)

x = 4

d)

none of these

55.

Solve: 7ⁿ⁺¹⁰−8 = 6

a)

n = -7.374

b)

n = -7.360

c)

n = -8.644

d)

n = -8.853

56.

Suppose a culture of bacteria begins with 500 cells and dies by 30% each year. Write an equation that represents this situation.

a)

y = 500(0.7)ⁿ

b)

y = 500(1.3)ⁿ

c)

y = 500(1.7)ⁿ

d)

y = 500(1.13)ⁿ

57.

Solve the following for the unknown value of x. Round your solution to two decimal places.
5 ln (3x - 2) = 15

a)

x = 1.24

b)

x = 7.36

c)

x = 217,935.16

d)

x = 6.03

58.

Solve for n:

2³ⁿ = 4

a)

n = 2

b)

n = 3

c)

n = 2/3

d)

n = 4

59.

Solve for x:

2^x+6=2⁵

a)

x = - 1

b)

x = 11

c)

x = 1

d)

x = - 11

60.

Solve: 9^8-x = 27^x-3

a)

x = 5

b)

x = -5

c)

x = 1/5

d)

x = -1/5

61.

Solve for b:

36^3b = 216^b+4

a)

b = 6

b)

b = 1

c)

b = 4

d)

b = - 4

62.

Write log_b(x/y) as two logs

a)

log_bx-log_by

b)

log_bx+log_by

c)

log_bx*log_by

d)

log_bx/log_by

63.

Solve the following for 'x';
log₆(3x - 2) = log₆(5x - 8)

a)

x = 3

b)

x = 2

c)

x = -1

d)

No Solution

64.

Use multiple log properties to write as a sum or difference of two logs: log(4x³)

a)

log 4 + 3log x

b)

3log 4 + 3log x

c)

3log 4 + log x

d)

log 12 + log x

65.

Use multiple log properties to write as a single log:
log₂x - 5log₂y

a)

log₂(x/y⁵)

b)

log₂(xy⁵)

c)

log₂(x/y)⁵

d)

log₂(x/5y)

66.

Solve for x: log₆x + log₆(x-5) = 2

a)

x = √7

b)

x = 9

c)

x = 4

d)

none of these

67.

To solve e^{4 – 3x}= x + 9 by graphing, which equations should be graphed?

a)

y = 0

b)

y = x + 9

c)

y = 4 - 3x

d)

y = e⁴

68.

Evaluate log₅20 to the third decimal place

a)

0.537

b)

2.996

c)

1.301

d)

1.861

69.

Evaluate log₄1

a)

1

b)

0

c)

4

d)

undefined

70.

e^ln(f)

a)

f

b)

e

c)

e^f

d)

undefined

71.

a)

A

b)

B

c)

C

d)

D

72.

Solve for x.

e^x+6 + 5 = 1

a)

x = - 4.614

b)

x = - 4.236

c)

No Solution

d)

x = - 0.334

73.

log (-1) =

a)

0.1

b)

.01

c)

all real numbers

d)

does not exist

74.

What is the asymptote of y = 2^x ?

a)

y = 0

b)

x = 0

75.

What is the asymptote of y = log₂x ?

a)

y = 0

b)

x = 0

76.

What is the asymptote of y = 2^x - 3

a)

y = 0

b)

y = -3

c)

x = 0

d)

x = -3

77.

What is the asymptote of y = log₂x - 3

a)

y = 0

b)

y = -3

c)

x = 0

d)

x = -3

78.

What is the asymptote of y = 2^x-3 ?

a)

y = 0

b)

y = -3

c)

x = 0

d)

x = -3

79.

What is the asymptote of y = log₂(x - 3) ?

a)

y = 0

b)

y = 3

c)

x = 0

d)

x = 3

80.

The asymptote of y = 2^x + 4 will shift...

a)

up four to y = 4

b)

down four to y = -4

c)

not shift at all and remain y = 0

81.

The asymptote of y = 2^x+5 will shift...

a)

up five to y = 5

b)

down five to y = -5

c)

will not shift and remain y = 0

82.

The asymptote of y = log₂x + 1 will shift...

a)

right one to x = 1

b)

left one to x = -1

c)

not shift at all and remain x = 0

83.

The asymptote of y = log₂(x + 2) will shift...

a)

right two to x = 2

b)

left two to x = -2

c)

not shift and remain x = 0

84.

Solve log(x) + log(x+3) = 1

a)

x = 5, 2

b)

x = 2, -5

c)

x = -5

d)

x = 2

85.

log₂(x + 2) + log₂x = 3

a)

x = -4, 2

b)

x = -2, 4

c)

x = 2

d)

x = 1

86.

log₅(4x - 7)=log₅(x + 5)

a)

x = 3

b)

x = 12

c)

x = 4

d)

x = 7

87.

Solve

a)

A

b)

B

c)

C

d)

D

88.

a)

x = 5

b)

x = 13

c)

x = 84

d)

x = -20

89.

a)

no solution

b)

x = 6

c)

x = 6 and -2

d)

x = -6, 2

90.

Solve for n:

2³ⁿ = 4

a)

n = 2

b)

n = 3

c)

n = 2/3

d)

n = 3/2

91.

Solve: 9^8-x = 27^x-3

a)

x = 5

b)

x = -5

c)

x = 1/5

d)

x = -1/5

92.

Use multiple log properties to write as a single log:

log₂x - alog₂y

a)

$\log_2\left(\frac{x}{y^a}\right)$

b)

$\log_2\left(\frac{x}{y}\right)^a$

c)

$\frac{\log_2x}{\log_2y^a}$

d)

$a\log\left(\frac{x}{y^a}\right)$

93.

Rewrite log_pt = m in exponential form.

a)

p^t = m

b)

t^m = p

c)

m^t = p

d)

p^m = t

94.

a)

A

b)

B

c)

C

d)

D

95.

Solve for x without using a calculator.

e^x+6 + 5 = 1

a)

x = -4.614

b)

$\ln\left(-4\right)\ -\ 6$

c)

No Solution

d)

$\log_e\left(-10\right)$

96.

Expand

a)

6log₈v-2log₈u

b)

6log₈u-2log₈v

c)

3log₈u-2log₈v

d)

6log₈u+2log₈v

97.

Use multiple log properties to write as a single log:

3log₂x - log₂y + log₂z

a)

$\log_2\left(\frac{x^3z}{y}\right)$

b)

$\log_2\left(\frac{3x^{ }z}{y}\right)$

c)

$\log_2\left(\frac{3x^{ }}{y}\right)z$

d)

$\log_2\left(\frac{x^3y}{z}\right)$

98.

Expand completely: log(2x⁵)

a)

log 2 + 5log x

b)

5log 2 + 5log x

c)

5log 2 + log x

d)

log 10 + log x

99.

What is the equation of the asymptote?

a)

x = -3

b)

x=5

c)

y= -3

d)

y=5

100.

Logarithmic functions are the inverse of...

a)

Linear Functions

b)

Exponential Functions

c)

Quadratic Functions

d)

Polynomial Functions

Alg 2 Ch. 6 Exponential & Logarithmic Functions

Total questions: 100

Worksheet time: 6hrs 39mins

Similar Resources on Wayground