Free Printable SubW 031125

1.

Expand

a)

A

b)

B

c)

C

d)

D

2.

Expand

a)

A

b)

B

c)

C

d)

D

3.

Expand

a)

log₈x + log₈y + log₈z

b)

5log₈x + 5log₈y + 5log₈z

c)

log₈xy + 5log₈z

d)

log₈x + log₈y + 5log₈z

4.

Expand

a)

5log₅ a - 6log₅b

b)

5log₅ a - 30log₅b

c)

5log₅ a + 30log₅b

d)

30log₅ b - 5log₅ a

5.

Expand the following: $\log_7\left(4x\right)$

a)

$\log_7\left(4\right)+\log_7\left(x\right)$

b)

$\log_7\left(4\right)-\log_7\left(x\right)$

c)

$\log_7\left(x^4\right)$

d)

$4\log_7\left(x\right)$

6.

Expand the following: $\log_5\left(z^8\right)$

a)

$5\log_8\left(z\right)$

b)

$8\log_5\left(z\right)$

c)

$\log_5\left(8z\right)$

d)

$8+\log_5\left(z\right)$

7.

Expand the following: $\log\left(j^4k^7\right)$

a)

$\log\left(4j\right)+\log\left(7k\right)$

b)

$11\log\left(j+k\right)$

c)

$28\log\left(jk\right)$

d)

$4\log\left(j\right)+7\log\left(k\right)$

8.

Rewrite the equation into logarithmic form:
6² = 36

a)

log₆ 2 = 36

b)

log₆ 36 = 2

c)

ln 36 = 2

d)

6³⁶ = 2

9.

a)

A

b)

B

c)

C

d)

D

10.

a)

A

b)

B

c)

C

d)

D

11.

a)

A

b)

B

c)

C

d)

D

12.

$\log_nn=$ (a)

13.

$\log_{9000}1=$ (a)

14.

log(x+6) = 1

a)

4

b)

4.222

c)

-5

d)

-9.550

15.

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

16.

Evaluate.
log₃81

a)

4

b)

¹/₄

c)

-4

d)

-¹/₄

17.

Write the following equation in exponential form:
log₂32 = 5

a)

2⁵ = 32

b)

2³² = 5

c)

5² = 32

d)

32² = 5

18.

Change to Exponential Form:
log₆36 = 2

a)

2⁶=36

b)

6²=36

c)

36²=6

d)

36⁶=2

19.

Evaluate the following logarithm:

log₃27

a)

3

b)

2

c)

-3

d)

¹/₃

20.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

21.

Choose the correct expanded natural logarithm:

$\ln(x^7)$

a)

$\ln(7x)$

b)

$\ln7+\ln x$

c)

$x\ln7$

d)

$7\ln x$

22.

The natural logarithm has what base?

a)

10

b)

0

c)

e

d)

-e

23.

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

24.

Solve for x:
5 e^6x+3= 0.1

a)

-1.152

b)

0.232

c)

-3.077

d)

-0.854

25.

Simplify e^ln(x)

a)

0

b)

1

c)

x

d)

8

26.

Rewrite in exponential form:
ln(2) = x

a)

2^x= 10

b)

10² = x

c)

e^x= 2

d)

e² = x

27.

Write the equation in exponential form.
$\ln87=x+4$

a)

$e^{\left(x+4\right)}=87$

b)

$e^{87}=x+4$

28.

Condense the expression as a single logarithm.

$\ln4+\ln3x$

a)

$\ln7x$

b)

$\ln\left(3x\right)^4$

c)

$\ln12x$

29.

Rewrite log_b(xⁿ)

a)

nlog_bx

b)

(log_bx)ⁿ

c)

xⁿlog_bx

d)

log_b(xⁿ)

30.

Write the expression as a single logarithm. Then simplify if possible.
log₅3 + log₅6 + log₅9

a)

log₅69

b)

log₅56

c)

log₅162

d)

log₅98

31.

Write the expression as a single logarithm. Then simplify if possible.
log 6 - log 3 + 2 log 7

a)

log 98

b)

log 78

c)

log 56

d)

log 45

32.

The common logarithm has what base?

a)

10

b)

0

c)

e

d)

-e

33.

Evaluate log_b(b)

a)

-1

b)

0

c)

1

d)

b

34.

The common logarithm is represented as what?

a)

log

b)

ln

35.

The natural logarithm is represented as what?

a)

log

b)

ln

36.

How are exponentials and logarithms related?

a)

They're cousins

b)

They're inverses

c)

They're not related

d)

They're reciprocals

37.

Without using a calculator, give the value of the following logarithm.

$\log_{ }10^{21.8}$

(a)

38.

Use a calculator to find the common logarithm. (Round to four decimal places as needed).

log(86)

(a)

39.

Use a calculator to find the common logarithm. (round to four decimal places as needed.)

log(55.8)

(a)

40.

Use a calculator to find the natural logarithm, base e. (Round to four decimal places as needed)

ln(42.11)

(a)

41.

Use a calculator to find the natural logarithm, base e. (Round to four decimal places as needed.

ln(0.0641)

(a)

42.

Use a calculator to find the natural logarithm, base e. (Round to four decimal places as needed)

ln(993.8)

(a)

43.

Use a calculator to find approximations of the common logarithms. (Round to four decimal places as needed)

log(25.46)

(a)

44.

Use a scientific calculator to solve the following equation for x.

$5^x=20$

Round to three decimal places

(a)

45.

Solve for x.

$4^{2x}=31$

(Round to 4 decimal places if needed)

(a)

46.

How much money will there be in an account at the end of 10 years if $17000 is deposited at 3% interest compounded quarterly? (Assume no withdrawals are made.)

(a)

47.

How much money will there be in an account at the end of 8 years if $5000 is deposited at 5.5% annual rate that is compounded continuously? (Assume no withdrawals are made.)

(a)

48.

Find the balance in the account after the given period.

$12,000 principal earing 4.8% compounded annually after 7 years.

a)

$3,243.19

b)

$16,661.35

c)

$15,243.19

d)

$4,661.35

49.

Find the balance in the account after the given period.

$5000 deposit earning 1.5% compounded quarterly after 3 years

a)

$5,229.70

b)

$7,604.38

c)

$7,777.27

d)

$5,538.86

50.

$3^2\times3^{8\ }=\$

a)

$3^6$

b)

$3^{16}$

c)

$3^{10}$

51.

True or False:

a)

True

b)

False

52.

According to exponent rules, when we multiply two power with the same base we _______ the exponents.
Example: c⁶ ⋅ c⁴

a)

add

b)

subtract

c)

multiply

d)

divide

53.

According to exponent rules, when we divide two powers with the same base we _______ the exponents.
Example: h⁸/h³

a)

add

b)

subtract

c)

multiply

d)

divide

54.

Write the exponent form of this expression: (x⋅x⋅x)⋅(x⋅x)

a)

3x⋅2x

b)

5x

c)

x⁵

55.

Simplify the expression:
c⁴⋅c³=

a)

^c12

b)

c⁴⁺³

c)

c⁷

56.

-4x⁰

a)

-4x

b)

-4

c)

1

d)

-1

57.

Simplify

(2a²b⁴z)(6a³b²z⁵)

a)

8a⁵b⁶z⁶

b)

12a⁶b⁸z⁵

c)

12a⁵b⁶z⁶

d)

8a⁶b⁸z⁵

58.

Simplify the expression. Write your answer using exponents.

x\cdot x^7\cdot x^3

a)

$x^{11}$

b)

$x^{10}$

c)

$x^{21}$

59.

Simplify: $\left(5x^3\right)\left(-3x^5\right)$

a)

$-15x^8$

b)

$2x^8$

c)

$-15x^2$

d)

$-15x^{-2\ }$

60.

a)

y¹⁴

b)

y¹⁰

c)

1¹⁴

d)

1¹⁰

61.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

62.

$\left(21x^2\right)\left(x^0\right)$

a)

$21x^2$

b)

$1$

c)

$0$

d)

$21x^{0\ }$

63.

a)

b)

c)

d)

64.

In order to multiply powers with the same base, we add their exponents.

a)

True

b)

False

65.

Simplify 4^-2=

a)

1/16

b)

-16

c)

1/4

d)

-42

66.

x^-3

a)

-x³

b)

1 / x³

c)

1 / x^-3

d)

-x^-3

67.

Re-write the expression in radical form.
x^2/3

a)

(∛x)²

b)

√x³

c)

(1/x)

d)

∛x

68.

Write the following expression in radical form:

a)

a.)

b)

b.)

c)

c.)

d)

d.)

69.

Write the following expression in radical form:

a)

a.)

b)

b.)

c)

c.)

d)

d.)

70.

Write the following expression in exponential form:

a)

a.)

b)

b.)

c)

c.)

d)

d.)

71.

What is 7¹?

a)

1

b)

7

c)

0

d)

14

72.

Write the expression in exponential form:
√23

a)

23^1/2

b)

23^-1/2

c)

23²

d)

23^-2

73.

Write the expression in exponential form:
∛x²

a)

x^3/2

b)

x^2/3

c)

x^1/2

d)

x^1/3

74.

Write the expression in exponential form:
∜x⁵

a)

x^4/5

b)

x^5/4

c)

x⁵

d)

x^1/4

75.

Write the expression in radical form.
x^3/4

a)

∜x³

b)

∛x⁴

c)

x^.75

d)

√x²

76.

Write the expression in radical form.
x^7/2

a)

√x⁷

b)

7√x²

c)

7x²

d)

∛x⁷

SubW 031125

Total questions: 76

Worksheet time: 4hrs 14mins

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