Free Printable Logarithm Laws

1.

a)

A

b)

B

c)

C

d)

D

2.

a)

A

b)

B

c)

C

d)

D

3.

Condense

a)

log(xyz³)

b)

log(xy/z³)

c)

log(x)+log(y)+log(z³)

d)

log(x³y³z³)

4.

Expand

a)

log₈x+log₈y+log₈z

b)

5log₈x+5log₈y+5log₈z

c)

log₈xy+5log₈z

d)

log₈x+log₈y+5log₈z

5.

Condense

a)

log₈(a¹⁸/b³)

b)

log₈(a¹⁸b³)

c)

log₈(a/b³)

d)

15log₈(a/b³)

6.

Expand

a)

A

b)

B

c)

C

d)

D

7.

The common logarithm has what base?

a)

10

b)

0

c)

e

d)

-e

8.

Expand the following logarithm:
log₂ 5x.

a)

log₂ 5 - log₂ x

b)

log₂ 5 + log₂ x

c)

2log 5 + 2log x

d)

log5 2 + log_x 2

9.

Expand the following logarithm:
log₃ 10z

a)

log₃ 10 - log₃ z

b)

log₃ 10 + log₃ z

c)

zlog₃ 10

d)

log₃ z¹⁰

10.

Expand the following logarithm:
log₂ 6/y

a)

log₂ 6 - log₂ y

b)

log₂ y - log₂ 6

c)

2log 6 + 2log y

d)

log₂ 6 - y

11.

Expand the following logarithm:

$\log_b\left(\frac{x^2y}{z^3}\right)$

a)

$\log_b\left(2x\right)+\log_b\left(y\right)+\log_b\left(3z\right)$

b)

$2\log_b\left(x\right)+\log_by-3\log_bz$

c)

$2\log_b\left(x\right)+\log_by+3\log_bz$

d)

$2\log_b\left(x\right)-\log_by-3\log_bz$

12.

Condense the following logarithm:

3 log₂x + 2 log₂y – 4 log₂z

a)

log₂(x³y²/z⁴)

b)

log₂(x³y²z⁴)

c)

log₂(xyz⁹)

d)

9log₂(xyz)

13.

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)

14.

Choose the answer that is equivalent.

\frac{1}{2}\log\left(x\right)=

a)

$\log\left(\sqrt{x}\right)$

b)

$\log\left(\frac{1}{2}x\right)$

c)

$\log\left(x^2\right)$

d)

$\log\left(\frac{1}{x^2}\right)$

15.

Choose the answer that is equivalent.

\frac{1}{3}\log\left(x\right)=

a)

$\log\left(^3\sqrt{x}\right)$

b)

$\log\left(\frac{x}{3}\right)$

c)

$\log\left(x^3\right)$

d)

$\log\left(\frac{1}{x^3}\right)$

16.

Choose the answer that is equivalent.

\frac{1}{3}\log\left(x\right)+\frac{1}{2}\log y

a)

$\log\left(^3\sqrt{x}\right)+\sqrt{y}$

b)

$\log\left(^3\sqrt{x}\cdot\sqrt{y}\right)$

c)

$\log\left(^3\sqrt{x}+\sqrt{y}\right)$

d)

$\log\left(\frac{x}{3}\cdot\frac{y}{2}\right)$

17.

Expand and FULLY simplify:

\log\left(100\sqrt{z}\right)

a)

$2+\frac{1}{2}\log\left(z\right)$

b)

$\log\left(100\right)+\frac{\log\left(z\right)}{2}$

c)

$100+\sqrt{z}$

d)

$\log\left(100\right)+\log\left(\sqrt{z}\right)$

18.

a)

A

b)

B

c)

C

d)

D

19.

a)

A

b)

B

c)

C

d)

D

20.

After condensing $\log_4\left(9\right)+\log_4\left(8\right)-\log_4\left(4.5\right)$ , it is equivalent to TWO of the following choices. Which ones?

a)

2

b)

$\log_4\left(16\right)$

c)

$\log_4\left(12.5\right)$

d)

4

Logarithm Laws

Total questions: 20

Worksheet time: 47mins

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