Free Printable Quiz: Properties of Logs

1.

log(4x)

a)

log4-logx

b)

log4+logx

c)

4logx

d)

xlog4

2.

log(xy²)

a)

logx+2logy

b)

logx+logy²

c)

logx-2logy

d)

logx+logy+log2

3.

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

a)

logx+logy

b)

xlogy

c)

log(x-y)

d)

logx-logy

4.

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

a)

logm-log3-logn

b)

3logm+logn

c)

3logm-logn

d)

3log(m-n)

5.

a)

log (xy³)

b)

log (x⁶− y³)

c)

log (x⁶/y³)

d)

log (x⁶ + y³)

6.

$\log\left(\frac{8x}{yz}\right)\$

a)

log8+logx-logy-logz

b)

log8+logx-logy+logz

c)

log(8x)-log(yz)

d)

8logx-ylogz

7.

a)

6log₈(xyz)

b)

log₈(x) - log₈(y) - 6log₈(z)

c)

log₈(x) + log₈(y) - log₈(z)

d)

log₈(x) + log₈(y) + 6log₈(z)

8.

Write as a single log: log 12 + 2 log x

a)

log (12 + 2x)

b)

log (14x)

c)

log (12 * 2x)

d)

log (12x²)

9.

Use the change of base property to rewrite as a single logarithm:

$\frac{\log15}{\log3}$

a)

$\log\ \frac{1}{5}$

b)

$\log5$

c)

$\log_{15}3$

d)

$\log_315$

10.

Condense: $\frac{1}{2}\log_3x\ +\ 5\log_3y$

a)

$\log_3\left(\sqrt{x}y^5\right)$

b)

$\log_3\left(\sqrt{x}y^5\right)$

c)

$\log_3\left(5\sqrt{x}y\right)$

d)

$\log_3\left(xy\right)^{\frac{5}{2}}$

11.

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)

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

12.

Condense

a)

logxyz³

b)

log(xy/z³)

c)

logx+logy+logz³

d)

logx³y³z³

13.

a)

A

b)

B

c)

C

d)

D

14.

True or False: $\log_xx\ =\ 1$

a)

False

b)

True

15.

$\ln\ \left(x\right)\ =\ ?$

a)

$\log_7\left(x\right)$

b)

$\log_{10}\left(x\right)$

c)

$\log_e\left(x\right)$

d)

$\log\left(x\right)$

16.

Expand: $\log_9\sqrt{23}$

a)

$\frac{1}{2}\log_923$

b)

$\log_9\left(\frac{1}{2}\right)-\log_923$

c)

$\log_9\sqrt{2}+\log_9\sqrt{3}$

d)

$\log_9\ \left(\frac{1}{2}\right)+\log_923$

17.

Condense: $4\log p+2\log q-3\log r$

a)

$\log\ p^4q^2r^3$

b)

$\log\ \frac{p^4}{q^2r^3}$

c)

$\log\ \frac{8pq}{3r}$

d)

$\log\ \frac{p^4q^2}{r^3}$

18.

Simplify: $\log_7\left(3\right)+\log_7\left(6\right)$

a)

$\log_79$

b)

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

c)

$\log_718$

d)

undefined

19.

Evaluate.

$\log_61$

(a)

20.

a)

A

b)

B

c)

C

d)

D

Quiz: Properties of Logs

Total questions: 20

Worksheet time: 1hrs 7mins

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