Free Printable Unit 7 Review (Logs & Exp.)

1.

Rewrite log₂8 = 3 in exponential form.

a)

2⁸ = 3

b)

2³ = 8

c)

3² = 8

d)

8³ = 2

2.

Write 2³= 8 in logarithmic form.

a)

log₂ 8 = 3

b)

log₂ 3 = 8

c)

log₃ 8 = 2

d)

log₃ 2 = 8

3.

Write 10⁴= 10000 in logarithmic form.

a)

log₁₀ 4 = 10000

b)

log₁₀₀₀₀ 4 = 10

c)

log₁₀ 10000 = 4

d)

log₄ 10000 = 10

4.

Write log₆ 216 = 3 in exponential form.

a)

3⁶=216

b)

6³=216

c)

216⁶=3

d)

3²¹⁶=6

5.

Evaluate log₇ 343

a)

3

b)

49

c)

7

d)

1

6.

Evaluate log₈ 8

a)

8

b)

-1

c)

0

d)

1

7.

Evaluate: log₆₄4 = x

a)

x = 3

b)

x = -3

c)

x = ⅓

d)

x = -⅓

8.

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

9.

Convert 10^(x+5)=100 to logarithmic form.

a)

log₁₀₀=x+5

b)

log(x+5)=100

c)

log(100)=x+5

d)

log_(x+5)(100)=10

10.

Convert log(x)=y+2 to exponential form.

a)

10^(y+2)=x

b)

1^x=y+2

c)

10^x=y+2

d)

x^(y+2)=10

11.

Solve for x:
log₄ x = 3

a)

4

b)

12

c)

32

d)

64

12.

log₅(4x-7)=log₅(x+5)

a)

3

b)

12

c)

4

d)

7

13.

log₉(x)+log₉(x+2)=log₉(35)

a)

5

b)

-7

c)

5, -7

d)

-7, -13

14.

3^{2x – 6} = 81

a)

x = log 4

b)

x = 5

c)

x = 4

d)

x = -1

15.

Solve the equation for x.

a)

22.198

b)

e

c)

1.131

d)

21.66

16.

Solve the equation for x.

a)

7.389

b)

0.693

c)

0.0183

d)

6.581

17.

Expand the logarithm
log₁₀ 7x

a)

(log₁₀ 7)(log₁₀ x)

b)

log₁₀ 7 + log₁₀ x

c)

7log₁₀ x

d)

xlog₁₀ 7

18.

Condense the Logarithm $5\log_{ }a\ -\ 25\log_{ }b$

a)

$\log\ \left(a^5+b^{25}\right)$

b)

$\log\ \left(a^5-b^{25}\right)$

c)

$\log\ \left(ab\right)^{25}$

d)

$\log_{ }\ \left(\frac{a^5}{b^{25}}\right)$

19.

Condense $3\log_{ }x+4\log_{ }y\ +\log_{ }z$

a)

$\log_{ }\ x^3y^4z$

b)

$12\log_{ }\ xyz$

c)

$\log_{ }\ 3x4yz$

d)

logx³y³z³

20.

Simplify: $\log_4\left(x+4\right)-\log_4\left(x-5\right)$

a)

$\log_49$

b)

$\log_4\left(2x-1\right)$

c)

$\log_4\left(x^2-x-20\right)$

d)

$\log_4\left(\frac{x+4}{x-5}\right)$

21.

Simplify: $2\log_3\left(11x\right)$

a)

$\log_3\left(22x\right)$

b)

$\log_3\left(121x\right)$

c)

$\log_3\left(121x^2\right)$

d)

$\log_3\left(11x^2\right)$

22.

Simplify: $\frac{1}{4}\log_516+3\log_5x$

a)

$\log_5\left(4x^3\right)$

b)

$\log_5\left(2x^3\right)$

c)

$\log_5\left(6x\right)$

d)

$\log_5\left(\frac{2}{x^3}\right)$

23.

Simplify: $\frac{1}{4}\log_281+\frac{1}{2}\log_249$

a)

$\log_221$

b)

$\log_210$

c)

$\log_2\left(\frac{3}{7}\right)$

d)

$\log_244.75$

24.

Simplify: $\frac{1}{2}\log_964+\log_9x$

a)

$\log_9\left(32x\right)$

b)

$\log_9\left(8x\right)$

c)

$\log_9\left(\frac{8}{x}\right)$

d)

$\log_98x$

25.

Expand using the properties of Logaritms $\log_{ }\ \frac{x^3}{y^4z}$

a)

$\log_{ }x+4\log_{ }y\ +\log_{ }z$

b)

$3\log_{ }x-4\log_{ }y\ -\log_{ }z$

c)

$3\log_{ }x+4\log_{ }y\ +\log_{ }z$

d)

$3\log_{ }x-4\log_{ }y\ +\log_{ }z$

26.

Expand the logarithm.
$\log_4\sqrt{x^3y}$

a)

$\frac{1}{2}\log_4\left(x\right)-\frac{1}{2}\log_4\left(y\right)$

b)

$\frac{3}{2}\log_4\left(x\right)-\frac{1}{2}\log_4\left(y\right)$

c)

$\frac{1}{2}\log_4\left(x\right)-\log_4\left(y\right)$

d)

$\frac{3}{2}\log_4\left(x\right)-\log_4\left(y\right)$

27.

Expand the logarithm.
$\log\frac{x}{y^6}$

a)

$\log x+6\log y$

b)

$\log x-6\log y$

c)

$\log x+\log6y$

d)

$\log x-\log6y$

28.

Expand . $\log_6\left(\frac{5x^3}{y}\right)$

a)

$\log_65x^3-\log_6y$

b)

$\log_65+\log_6x^3-\log_6y$

c)

$\log_65+3\log_6x-\log_6y$

d)

$\log_65+3\log_6x+\log_6y$

29.

Write in exponential form.
log₂32 = 5

a)

2^-5 = 32

b)

2³² = 5

c)

2⁵ = 32

d)

32⁵ = 2

30.

What is the value of e^ln(5)

a)

e

b)

1

c)

5

d)

Does not exist

31.

What is the value of ln(e⁷)

a)

2.718...

b)

1

c)

7

d)

Does not exist

32.

Solve for x:
ln(x)=3

a)

e^x

b)

3e

c)

3^e

d)

e³

33.

Solve for x:
e^x=7

a)

x=ln7

b)

x=ln⁷

c)

x=7^ln

d)

No solution

34.

Change to Exponential Form:
log₆36 = 2

a)

2⁶=36

b)

6²=36

c)

36²=6

d)

36⁶=2

35.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

36.

Change to Logarithmic Form:
5³ = 125

a)

log ₅ 125 = 3

b)

log₃125 = 5

c)

log ₅ 3 =125

d)

log₁₂₅ 3 = 5

37.

Change to Exponential Form:
log₆36 = 2

a)

2⁶=36

b)

6²=36

c)

36²=6

d)

36⁶=2

38.

log₅25 = ?

a)

2

b)

5

c)

125

d)

10

39.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

40.

Expand: log(4x)

a)

log4-logx

b)

log4+logx

c)

4logx

d)

xlog4

41.

Rewrite as a single logarithm:

\log3\ +\ \log7

a)

log 10

b)

log 21

c)

log 3/7

d)

log 3/log 7

42.

Expand $\log_4\left(3xy\right)$

a)

$\log_4\left(3\right)\ +\ \log_4\left(x\right)-\ \log_4\left(y\right)$

b)

$3\log_4\left(x\right)\ +\ 3\log_4\left(y\right)$

c)

$\log_4\left(3\right)\ +\ \log_4\left(x\right)+\ \log_4\left(y\right)\$

d)

$4\log\left(3\right)\ +\ 4\log\left(x\right)+\ 4\log\left(y\right)\$

43.

Condense into a single logarithm.
$\log_25+\log_29+\log_2w$

a)

$\log_2\left(14w\right)$

b)

$\log_2\left(45w\right)$

c)

$\log_2\left(\frac{14}{w}\right)$

d)

$\log_2\left(14+w\right)$

44.

Expand: $\log\left(\frac{x}{y}\right)$

a)

logx+logy

b)

xlogy

c)

log(x-y)

d)

logx-logy

45.

Condense into one log: $2\log_3\left(x\right)+\log_3\left(y\right)$

Remember to use the power property first!

a)

$\log_3\left(2xy\right)\$

b)

$\log_3\left(x^2y\right)$

c)

$\log_3\left(xy\right)^2$

d)

$2\log_3\left(xy\right)$

46.

Expand: $\log\left(\frac{m^3}{n}\right)$

a)

logm-log3-logn

b)

3logm+logn

c)

3logm-logn

d)

3log(m-n)

47.

log₂(x + 2) + log₂x = 3

a)

-4, 2

b)

-2, 4

c)

2

d)

1

48.

log₅(4x-7)=log₅(x+5)

a)

3

b)

12

c)

4

d)

7

49.

log₄(3x-1)=log₄(2x+3)

a)

4

b)

3

c)

1

d)

8

50.

log₂(x+3)=4

a)

16

b)

13

c)

3

d)

10

Unit 7 Review (Logs & Exp.)

Total questions: 50

Worksheet time: 13hrs 30mins

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