Free Printable Unit 11 Part 1 Test Review

1.

Expand: log_b(xy)

a)

log_bx+log_by

b)

log_bx-log_by

c)

log_bx*log_by

d)

log_bx/log_by

2.

Expand:

\log_b\left(\frac{x}{y}\right)

a)

log_bx-log_by

b)

log_bx+log_by

c)

log_bx*log_by

d)

log_bx/log_by

3.

Condense:

log₅3 + log₅6 + log₅9

a)

log₅69

b)

log₅56

c)

log₅162

d)

log₅98

4.

Expand

a)

A

b)

B

c)

C

d)

D

5.

a)

log₅(x²z²y¹⁰)

b)

log₅(z²y²x¹⁰)

c)

log(zy²x¹⁰)

d)

log₅(z² + y²+ x¹⁰)

6.

Condense

a)

A

b)

B

c)

C

d)

D

7.

Expand

a)

A

b)

B

c)

C

d)

D

8.

Write in exponential form

a)

A

b)

B

c)

C

d)

D

9.

When you have two log expressions separated by a minus sign (-), we really need to ___________ them to simplify into one log expression.

a)

add

b)

subtract

c)

multiply

d)

divide

10.

When you have a log expression with a number in front of it, we really need to ___________ .

a)

make the number an exponent at the end of the log expression.

b)

multiply it with the log expression.

c)

add it to the log expression.

d)

subtract it from the log expression.

11.

When you have two log expressions separated by a plus sign (+), we really need to ___________ them to simplify into one log expression.

a)

add

b)

subtract

c)

multiply

d)

divide

12.

Condense: $\log_4\left(x+4\right)-\log_4\left(x-5\right)$

a)

$\log_49$

b)

$\log_4\left(2x-1\right)$

c)

$\log_4\left(x^2-x-20\right)$

d)

$\log_4\left(\frac{x+4}{x-5}\right)$

13.

a)

24log(u) - log(v)

b)

24log(u) + 6log(v)

c)

4log(u) + 6log(v)

d)

4log(u) - 6log(v)

14.

Write in exponential form.
log₂32 = 5

a)

2^-5 = 32

b)

2³² = 5

c)

2⁵ = 32

d)

32⁵ = 2

15.

Expand: $\log_4\left(3x^2\right)$

a)

$2\log_43x$

b)

$2\log_43\ +\ 2\log_4x$

c)

$\log_43\ +\ 2\log_4x$

d)

$2\log_43\ +\ \log_4x$

16.

$\log_p\left(t\right)=m$ Rewrite in exponential form.

a)

$p^t=m$

b)

$t^m=p$

c)

$m^t=p$

d)

$p^m=t$

17.

Expand: $\log_7\ y^8$

a)

$\log_7y\ +\ \log_78$

b)

$\log_7y-\log_78$

c)

$8\log_7y$

d)

$\log_78+\log_7y$

18.

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

a)

$3\log2\ -\ \log k$

b)

$3\log k-\log2$

c)

$3\log k+\log2$

d)

$\log k-3\log2$

19.

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

a)

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

b)

$\log\ a\ -\ \log3b$

c)

$3\log a-\log b$

d)

$\log a+3\log b$

20.

Which of the following illustrates the Product Property of Logarithms

a)

log₃(x/y) = log₃(x) - log₃(y)

b)

log₃(xy) = log₃(x) - log₃(y)

c)

log₃(xy) = log₃(x) + log₃(y)

21.

State the property(s) used to expand the expression

\log_4\left(\frac{20}{x^3}\right)\ =\ \log_420-3\log_4x

a)

Power Property

b)

Quotient Property

c)

Quotient and Power Property

d)

Product and Power Property

22.

State the property (s) used to simplify the expression

6log 2 = log 64

a)

Product Property

b)

Quotient Property

c)

Power Property

d)

Product and Power Property

23.

State the property(s) used to expand the expression

\log_3\left(a^2b^5\right)\ =\ 2\log_3a+5\log_3b

a)

Power Property

b)

Quotient Property

c)

Quotient and Power Property

d)

Product and Power Property

24.

What is the base in the equation

log x = 3?

a)

x

b)

10

c)

3

d)

1

e)

0

25.

What is the quotient property of logarithms?

a)

$\log_bx^n=n\log_bx$

b)

$\log_b\left(\frac{x}{y}\right)=\log_bx\ -\log_by$

c)

$\log_b\ \left(x\cdot y\right)=\log_bx\ +\ \log_by$

26.

Evaluate

\log_464=

a)

3

b)

2

c)

4

d)

16

27.

Evaluate:
$\log_216^7$

a)

20

b)

28

c)

4

d)

5

28.

Which equation will help you solve for x?
$\log_6\left(3x+2\right)=\log_6\left(5x-8\right)$

a)

$3x+2+5x-8=0$

b)

$6^{\left(5x-8\right)}=3x+2$

c)

$3x+2=5x-8$

d)

No equation will help you

29.

Which equation will help you solve for x?

\log_3\left(8\right)+\log_3\left(2x\right)=5

a)

$\frac{1}{4}x=5$

b)

$3^5=16x$

c)

$16x=5$

d)

$3^5=4x$

30.

Which equation will help you solve for x?
$\log\left(3x+25\right)=2$

a)

$3x+25=2$

b)

$2^2=3x+25$

c)

No equation will help you

d)

$10^2=3x+25$

31.

Which equation will help you solve for x?

a)

$x+2=3$

b)

$2x=3$

c)

$2^3=x+2$

d)

$10^3=x+2$

32.

Which equation will help you solve for x?

\log_2\left(x-4\right)=6

a)

x - 4 = 6²

b)

6₂ = x - 4

c)

2^(x-4) = 6

d)

2⁶ = x - 4

33.

log₅(4x-7)=log₅(x+5)

a)

3

b)

12

c)

4

d)

7

34.

log₈(4x+4)=2

a)

15

b)

12

c)

10

d)

3

35.

Solve for x:

log₂(x+3)=4

a)

16

b)

13

c)

3

d)

10

36.

Solve for x:

\log_{10}\left(x+6\right)=1

a)

4

b)

4.222

c)

-5

d)

-9.550

37.

solve for x

\log_7\left(3x-2\right)=2

a)

x = 16/3

b)

x = 16

c)

x = 3/4

d)

x = 17

38.

Solve for f:
$\log_6\left(f-4\right)=\log_6\left(6f+26\right)$

a)

f = -5

b)

f = 5

c)

f = 6

d)

f = -6

39.

Solve the equation:
$\log_2\left(7x-4\right)=\log_2\left(3+8x\right)$

a)

x = 7

b)

x = -7

c)

x = 2/7

d)

x = 11

40.

Solve:

$\log_2\left(x+3\right)=5$

a)

x=2

b)

x=29

c)

x=7

d)

x=32

Unit 11 Part 1 Test Review

Total questions: 40

Worksheet time: 3hrs 20mins

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