Free Printable Log Properties Mixed Practice

1.

Use the properties of logs to write the expression as a single log.

$\log\left(12x^2\right)-\log\left(6x\right)$

a)

$\log\left(72x^2\right)$

b)

$\log\left(12x^2-6x\right)$

c)

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

d)

$\log\left(18x\right)$

2.

Use the properties of logs to write the expression as a single log.

$\log\left(5x\right)+\log\left(4\right)$

a)

$\log\left(20x\right)$

b)

$\log\left(9x\right)$

c)

$\log\left(x\right)$

d)

$\log\left(5x+4\right)$

3.

Use the properties of logs to condense the expression into a single log.

$\log\left(6\right)+\log\left(3x\right)-\log\left(2\right)$

a)

$\log\left(9x\right)$

b)

$\log\left(6x\right)$

c)

$\log\left(4x\right)$

d)

$\log\left(7x\right)$

4.

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

5.

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

6.

Rewrite log_b(xⁿ)

a)

n log_bx

b)

(log_bx) ⁿ

c)

xⁿlog_bx

d)

log_b(xⁿ)

7.

Condense

a)

A

b)

B

c)

C

d)

D

8.

a)

log₅(x²z²y¹⁰)

b)

log₅(z²y²x¹⁰)

c)

log(zy²x¹⁰)

d)

log₅(z² + y²+ x¹⁰)

9.

a)

6 log₈(xyz)

b)

log₈(x) - log₈(y) - 6log₈(z)

c)

log₈(x) + log₈(y) - log₈(z)

d)

log₈(x) + log₈(y) + 6log₈(z)

10.

a)

5log₆(a) + 6log₆(c) − 30log₆(b)

b)

log₆(a) + 6log₆(c) − 5log₆(b)

c)

6log₆(a) − 6log₆(c) − 30log₆(b)

d)

6log₆(a) + 6log₆(c) − 30log₆(b)

11.

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)

12.

a)

60 log(ab)

b)

6log(a) + log(b)

c)

log(a) - 30 log(b)

d)

6log(a) + 30 log(b)

13.

$\log_3\left(2\right)+\log_3\left(5x\right)-\log_3\left(7\right)=$

a)

$\log_3\left(70x\right)$

b)

$\log_3\left(10x-7\right)$

c)

$\log_3\left(\frac{10x}{7}\right)$

d)

$\log_3\left(\frac{5x^2}{7}\right)$

14.

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

a)

log₅69

b)

log₅56

c)

log₅162

d)

log₅98

15.

When a logarithm has division inside of it, it expands using ________________.

a)

Addition

b)

Subtraction

c)

Multiplication

d)

Division

16.

a)

log (xy³)

b)

log (x⁶− y³)

c)

log (x⁶/y³)

d)

log (x⁶ + y³)

17.

a)

F

b)

G

c)

H

d)

J

18.

a)

A

b)

B

c)

C

d)

D

19.

a)

F

b)

G

c)

H

d)

J

20.

Select all that apply.

What rule/rules would you use to condense the following expression?

$\log_3𝑝+2\log_3q$

a)

Power Rule

b)

Product Rule

c)

Quotient Rule

d)

None of the above

21.

Select all that apply.

What rule/rules would you use to condense the following expression?

$6\log_5u-10\log_5v$

a)

Power Rule

b)

Product Rule

c)

Quotient Rule

d)

None of the above

22.

Select all that apply.

What rule/rules would you use to condense the following expression?

$\frac{1}{2\ }\log_5144$

a)

Power Rule

b)

Product Rule

c)

Quotient Rule

d)

None of the above

23.

Select all that apply.

What rule/rules would you use to condense the following expression?

$5\log a+2\log b-3\log c$

a)

Power Rule

b)

Product Rule

c)

Quotient Rule

d)

None of the above

24.

Select all that apply.

What rule/rules would you use to expand the following expression?

$\log_7q^{\frac{1}{8}}$

a)

Power Rule

b)

Product Rule

c)

Quotient Rule

d)

None of the above

25.

Select all that apply.

What rule/rules would you use to expand the following expression?

$\log\left(\frac{ab^3}{c^4}\right)$

a)

Power Rule

b)

Product Rule

c)

Quotient Rule

d)

None of the above

26.

Select all that apply.

What rule/rules would you use to expand the following expression?

$\log_7p^6q^3r^{\frac{1}{4}}$

a)

Power Rule

b)

Product Rule

c)

Quotient Rule

d)

None of the above

27.

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

a)

logm-log3-logn

b)

3logm+logn

c)

3logm-logn

d)

3log(m-n)

28.

Expand.

a)

A

b)

B

c)

C

d)

D

29.

a)

A

b)

B

c)

C

d)

D

30.

a)

log (xy³)

b)

log (x⁶− y³)

c)

log (x⁶/y³)

d)

log (x⁶ + y³)

31.

Condense: log16 + log2 - log8

a)

log4

b)

log8

c)

log10

d)

log24

32.

$\ln\left(\frac{2x^2y}{z^4}\right)$

a)

ln2+2lnx+lny+4lnz

b)

ln2+2lnx+lny-4lnz

c)

2ln(2xy)-4lnz

d)

2ln2x+lny-4lnz

33.

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)

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

34.

Expand the Log completely and simplify if possible. $\log_{ }\left(\frac{x^{\frac{1}{2}}}{z^5y}\right)$

a)

$\frac{1}{2}\log x\ -5\log z-\log y$

b)

$\log\ x^{\frac{1}{2}\ }-\log\ z^5+\log\ y$

c)

$\log\ \sqrt{x}-\log z^5+y^{ }$

d)

$10\log\ x-z+y$

35.

Use properties of Logs to write $\log_3\left(4\right)+\log_3\left(y\right)-\log_3\left(x\right)$

as one Log

a)

$\log_3\left(\frac{4x}{y}\right)\$

b)

$\log_3\left(4xy\right)$

c)

$\log_3\left(\frac{4}{xy}\right)$

d)

$\log_3\left(\frac{4y}{x}\right)$

36.

Logarithmic functions are the inverse of...

a)

Linear Functions

b)

Exponential Functions

c)

Quadratic Functions

d)

Polynomial Functions

37.

Rewrite log₃t = 5 in exponential form.

a)

5^t=3

b)

log₃5 = log₃t

c)

t⁵=3

d)

3⁵=t

38.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

39.

Use multiple log properties to write as a single log:
log₂x - 5log₂y

a)

log₂(x/y⁵)

b)

log₂(xy⁵)

c)

log₂(x/y)⁵

d)

log₂(x/5y)

40.

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)

Log Properties Mixed Practice

Total questions: 40

Worksheet time: 3hrs 32mins

Similar Resources on Wayground