Free Printable Log Properties (Expand and Condense)

1.

Expand $\log_4\left(6y\right)$

a)

$\log_4\left(6\right)\ +\ \log_4\left(y\right)$

b)

$\log_4\left(6\right)\ -\ \log_4\left(y\right)$

c)

$y\log_4\left(6\right)\$

d)

$\log_4\left(\frac{6}{y}\right)\$

2.

Expand $\log_2\left(3y^2\right)$

a)

$\log_2\left(3\right)\ +\ \log_2\left(y\right)$

b)

$2\log_2\left(3\right)\ +\ 2\log_2\left(y\right)$

c)

$\log_2\left(3\right)\ +\ 2\log_2\left(y\right)$

d)

$\log_2\left(\frac{3}{y^2}\right)\$

3.

Expand $\log_2\left(\frac{x}{3y}\right)$

a)

$\log_2\left(x\right)\ +\ \log_2\left(3\right)\ +\ \log_2\left(y\right)$

b)

$3\log_2\left(x\right)\ +\ \log_2\left(y\right)$

c)

$\log_2\left(x\right)\ -\ 3\log_2\left(y\right)$

d)

$\log_2\left(x\right)\ -\ \log_2\left(3\right)\ -\ \log_2\left(y\right)$

4.

Use properties of Logs to write $2\log_3\left(x\right)+\log_3\left(y\right)$

as one Log

a)

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

b)

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

c)

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

d)

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

5.

Use properties of Logs to write $2\log_3\left(a\right)+2\log_3\left(b\right)$

as one Log

a)

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

b)

$\log_3\left(a^2b\right)$

c)

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

d)

$\log_3\left(a+b\right)^2$

6.

Condense

a)

A

b)

B

c)

C

d)

D

7.

Expand.

a)

A

b)

B

c)

C

d)

D

8.

Rewrite log₃t = 5 in exponential form.

a)

5^t=3

b)

log₃5 = log₃t

c)

t⁵=3

d)

3⁵=t

9.

log₃81 =

a)

2

b)

3

c)

4

d)

5

10.

log (-1) =

a)

0.1

b)

.01

c)

all real numbers

d)

does not exist

11.

Use the properties of logarithms to retwrite

a)

A

b)

B

c)

C

d)

D

12.

True or False:

log 12 - log 4 = log 8

a)

True

b)

False

13.

a)

ln(wvu⁵)

b)

ln(u + v + w⁵)

c)

ln(uvw⁵)

d)

ln(uvw)⁵

14.

Logarithmic functions are the inverse of...

a)

Linear Functions

b)

Exponential Functions

c)

Quadratic Functions

d)

Polynomial Functions

15.

Expand: $\log_b\ m^p$

a)

$\log_bm\ +\ \log_bp$

b)

$\log_bm-\log_bp$

c)

$\log_bp-\log_bm$

d)

$p\log_bm$

16.

Expand: $\log\ \frac{k}{d}$

a)

$k\log d$

b)

$\log k\ +\ \log\ d$

c)

$\log\ k\ -\ \log d$

d)

$\log d-\log k$

17.

Expand: $\log\ ab$

a)

$\log a\ -\ \log b$

b)

$b\log a$

c)

$a\log b$

d)

$\log a+\log b$

18.

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)

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

19.

Expand: $\log\ \frac{k^3}{2}$

a)

$3\log2\ -\ \log k$

b)

$3\log k-\log2$

c)

$3\log k+\log2$

d)

$\log k-3\log2$

20.

Expand: $\log\ \frac{a}{b^3}$

a)

$\log a\ -\ 3\log b$

b)

$\log\ a\ -\ \log3b$

c)

$3\log a-\log b$

d)

$\log a+3\log b$

21.

Expand: $\log_74\sqrt{d}$

a)

$\log_7\ 4\ -\ \frac{1}{2}\log_7\ d$

b)

$4\log_7d\ +\log_7\ \frac{1}{2}$

c)

$\log_7\ 4+\frac{1}{2}\log_7\ d$

d)

$\frac{1}{2}\log4d$

22.

Simplify the following: $\log_5\left(3\right)+\log_5\left(r\right)-\log_5\left(w\right)$

a)

$\log_5\left(3rw\right)$

b)

$\log_5\left(3+r-w\right)$

c)

$\log_5\left(\frac{3r}{w}\right)$

d)

$\frac{\log_5\left(3r\right)}{\log_5\left(w\right)}$

23.

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

a)

log (12 + 2x)

b)

log (14x)

c)

log (12 * 2x)

d)

log (12x²)

24.

Rewrite the equation in exponential form.
$\log_8\left(512\right)=3$

a)

$8^{512}=3$

b)

$3^8=512$

c)

$8^3=512$

d)

$3^{512}=8$

25.

Condense the expression to a single logarithm.
$8\log_2\left(p\right)+\log_2\left(t\right)$

a)

$\log_2\left(8pt\right)$

b)

$\log_2\left(p^8t\right)$

c)

$\log_2\left(pt^8\right)$

d)

$\log_2\left(\left(pt\right)^8\right)$

26.

Condense the expression to a single logarithm.
$\log_{14}\left(h\right)-6\log_{14}\left(j\right)$

a)

$\log_{14}\left(\frac{h}{j}\right)$

b)

$\log_{14}\left(\frac{h}{j^6}\right)$

c)

$\log_{14}\left(\frac{h^6}{j}\right)$

d)

$\log_{14}\left(\left(\frac{h}{j}\right)^6\right)$

27.

a)

log (xy³)

b)

log (x⁶− y³)

c)

log (x⁶/y³)

d)

log (x⁶ + y³)

28.

a)

log₅(x²z²y¹⁰)

b)

log₅(z²y²x¹⁰)

c)

log(zy²x¹⁰)

d)

log₅(z² + y²+ x¹⁰)

29.

a)

60 log(ab)

b)

6log(a) + log(b)

c)

log(a) - 30 log(b)

d)

6log(a) + 30 log(b)

30.

Log₂(16)

a)

2

b)

0

c)

4

d)

-2

31.

Log₃(–81)

a)

Undefined

b)

–4

c)

4

d)

9

32.

Condense: $2\log_5\left(x\right)+3\log_5\left(y\right)$

a)

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

b)

$\log_5\left(2x\right)+\log_5\left(3y\right)$

c)

$2\log_5\left(x\right)\cdot3\log_5\left(y\right)$

d)

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

33.

condense into one logarithm $2\log_5\ a+\log_5\ b-4\log_5\ c$

a)

$\log_5\left(\frac{a^2b}{c^4}\right)$

b)

$\log_5\left(\frac{ab}{c}\right)$

c)

$\log_5\left(a^2+b-c^4\right)$

d)

$-2\log_5\left(a+b-c\right)$

Log Properties (Expand and Condense)

Total questions: 33

Worksheet time: 3hrs 32mins

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