Free Printable Properties of Logarithms

1.

Condense

a)

logxyz³

b)

log(xy/z³)

c)

logx+logy+logz³

d)

logx³y³z³

2.

Expand

a)

log₈x+log₈y+log₈z

b)

5log₈x+5log₈y+5log₈z

c)

log₈xy+5log₈z

d)

log₈x+log₈y+5log₈z

3.

Expand

a)

A

b)

B

c)

C

d)

D

4.

Evaluate.
log₃81

a)

4

b)

¹/₄

c)

-4

d)

-¹/₄

5.

Expand

a)

A

b)

B

c)

C

d)

D

6.

Simplify: $\log_73+\log_76$

a)

$\log_79$

b)

$\log_7\left(\frac{1}{2}\right)$

c)

$\log_7729$

d)

undefined

7.

Write log_b(xy) as two logs

a)

log_bx+log_by

b)

log_bx-log_by

c)

log_bx*log_by

d)

log_bx/log_by

8.

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

9.

Rewrite log_b(xⁿ)

a)

nlog_bx

b)

(log_bx)ⁿ

c)

xⁿlog_bx

d)

log_b(xⁿ)

10.

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

a)

log₅69

b)

log₅56

c)

log₅162

d)

log₅98

11.

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

12.

Expand

a)

A

b)

B

c)

C

d)

D

13.

a)

6log₈(xyz)

b)

log₈(x) - log₈(y) - 6log₈(z)

c)

log₈(x) + log₈(y) - log₈(z)

d)

log₈(x) + log₈(y) + 6log₈(z)

14.

a)

log (a⁵+ b²⁵)

b)

log (a⁵− b²⁵)

c)

log (ab²⁵)

d)

log (a⁵/b²⁵)

15.

Condense

a)

A

b)

B

c)

C

d)

D

16.

Condense

a)

logxyz³

b)

log(xy/z³)

c)

logx+logy+logz³

d)

logx³y³z³

17.

a)

log(x) + log(z) + 4log(y)

b)

3log(x) − log(z) − 4log(y)

c)

3log(x) + log(z) + 4log(y)

d)

log(x) − 4log(z) − 3log(y)

18.

Rewrite as a single logarithm:

\log3\ +\ \log7

a)

log 10

b)

log 21

c)

log 3/7

d)

log 3/log 7

19.

Rewrite as a single logarithm:

\log_260\ -\ \log_210

a)

$\log_26$

b)

$\log_250$

c)

$\frac{\log_260}{\log_210}$

d)

$\log_270$

20.

Use the properties of logarithms to rewrite as the sum of two logarithms:

\log55

a)

log 40 + log 15

b)

log 50 + log 5

c)

log 11 + log 5

21.

Write in exponential form.
log₂32 = 5

a)

2^-5 = 32

b)

2³² = 5

c)

2⁵ = 32

d)

32⁵ = 2

22.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

23.

Solve for x
5^x = 17

a)

x = log₁₇5

b)

x = log 5 + log 17

c)

x = log₅17

d)

x = (log 5)/(log 17)

24.

Expand

a)

A

b)

B

c)

C

d)

D

25.

Expand

a)

A

b)

B

c)

C

d)

D

26.

Write as a single logarithm:

log(30)-log(6)

a)

-6log(30)

b)

log(24)

c)

log(-24)

d)

log(5)

27.

Rewrite in exponential form:
ln(2) = x

a)

2^x= 10

b)

10² = x

c)

e^x= 2

d)

e² = x

28.

Rewrite e^x = 9 using a logarithm

a)

ln x = 9

b)

ln 9 = x

c)

log_x e = 9

d)

log₉ x = e

Properties of Logarithms

Total questions: 28

Worksheet time: 2hrs 59mins

Similar Resources on Wayground