Free Printable Unit 5.2 Review

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Worksheets

Unit 5.2 Review

Total questions: 33

Worksheet time: 54mins

Name

Class

Date

1.

Rewrite in exponential form:
2=log₉x

a)

9^x=2

b)

2^x=9

c)

2⁹=x

d)

9²=x

2.

Write 6^x = 8 in log form.

a)

log₆ 8 = x

b)

log₈ 6 = x

c)

log₆ x = 8

d)

log₈ x = 6

3.

Write log5 = x in exponential form

a)

10^x = 5

b)

5^x = 1

c)

1^x = 5

d)

10⁵ = x

4.

Write 10 = 5^x in log form

a)

x = log 5

b)

x = log₅10

c)

x = 5 log10

d)

x = 10 log 5

5.

Rewrite log₃t = 5 in exponential form.

a)

5^t=3

b)

log₃5 = log₃t

c)

t⁵=3

d)

3⁵=t

6.

Write in logarithmic form:

a^b = c

a)

log _a c = b

b)

log _b c = a

c)

log _a b = c

d)

log _b a = c

7.

Change to logarithmic form.

3^h = w

a)

log_w3 = h

b)

log₃w = h

c)

log_h3 = w

d)

log₃h = w

8.

Convert 3^x = 12 to the equivalent log form.

a)

3¹² = x

b)

log_x3 = 12

c)

log₃x = 12

d)

log₃ 12 = x

9.

Change to exponential form.

log_a2 = 5

a)

a²= 5

b)

5² = a

c)

a⁵= 2

d)

2⁵ = a

10.

Logarithms are the inverse of ___________.

a)

Trees

b)

Quadratics

c)

Square

d)

Exponential

11.

Write 3 = 7^x in log form.

a)

log₇ 3 = x

b)

log₃ 7 = x

c)

log₇ x = 3

d)

log₃ x = 7

12.

Rewrite in exponential form: (remember base 10!)

log(7) = x

a)

7= 10^x

b)

10⁷ = x

c)

e^x= 7

d)

e⁷ = x

13.

$Evaluate\ \log_28$

(a)

14.

$Evaluate\ \log_864$

(a)

15.

$Evaluate\ \log_77$

(a)

16.

$Evaluate\ \log_381$

(a)

17.

$Evaluate\ \log_{10}1000$

(a)

18.

$Evaluate\ \log_61$

(a)

19.

$Evaluate\ \log_8\frac{1}{8}$

(a)

20.

$Evaluate\ \log_7\frac{1}{49}$

(a)

21.

$Evaluate\ \log_93$

(a)

22.

Expand

a)

6log₈v-2log₈u

b)

6log₈u-2log₈v

c)

3log₈u-2log₈v

d)

6log₈u+2log₈v

23.

Expand

a)

log₈x+log₈y+log₈z

b)

5log₈x+5log₈y+5log₈z

c)

log₈xy+5log₈z

d)

log₈x+log₈y+5log₈z

24.

Expand

a)

5log₅a - 6log₅b

b)

5log₅a - 30log₅b

c)

5log₅a + 30log₅b

d)

30log₅b - 5log₅a

25.

Write the expression as a single logarithm. Then simplify if possible.

log₅3 + log₅6 + log₅9

a)

log₅69

b)

log₅56

c)

log₅162

d)

log₅98

26.

Condense

a)

A

b)

B

c)

C

d)

D

27.

Condense

a)

A

b)

B

c)

C

d)

D

28.

Expand

a)

A

b)

B

c)

C

d)

D

29.

Expand

a)

A

b)

B

c)

C

d)

D

30.

$4\log_4u-6\log_4v$ Condense

a)

$\log_4\left(\frac{u}{v}\right)^{24}$

b)

$\log_4\left(\frac{u^6}{v^4}\right)^{ }$

c)

$\log_4\left(\frac{u^4}{v^6}\right)^{ }$

d)

$\log_4\left(\frac{v^6}{u^4}\right)^{24}$

31.

Expand $\log_4\left(x^5y^2\right)$

a)

$10\log_4\left(x\ +y\right)$ 1

b)

$5\log_4x+2\log_4y$

c)

$5\log_9x+2\log_9y$

d)

$\log_4\left(5x+2y\right)$

32.

$Expand\ \log_5\left(xy^5\right)^2$

a)

$2\log_5x\ +10\log_5y$

b)

$10\left(\log_5x\ +\log_5y\right)$

c)

$10\log_5x\ +10\log_5y$

d)

$10\log_5x\ +2\log_5y$

33.

Condense

a)

15log₈u+ 3log₈v

b)

15log₈u- 3log₈v

c)

log₈(u¹⁵/v³)

d)

log₈u¹⁵v³

100 %

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