Quiz about Evaluating Logarithms with Properties

Question 1

Write the following equation in exponential form:
log₂32 = 5

Accepted Answer

25 = 32

Answer

232 = 5

Answer

52 = 32

Answer

322 = 5

Question 2

log₂(x + 5) = 3

Accepted Answer

3

Answer

4

Answer

5

Answer

6

Question 3

log₂(x + 2) + log₂x = 3

Accepted Answer

2

Answer

-4, 2

Answer

-2, 4

Answer

1

Question 4

4^(x-2)= 64^(x+1)

Accepted Answer

-5/2

Answer

-2/5

Answer

7/2

Answer

2/7

Question 5

Write log_b(xy) as two logs

Accepted Answer

log_bx+log_by

Answer

log_bx-log_by

Answer

log_bx*log_by

Answer

log_bx/log_by

Question 6

Condense: log₂6+log₂3=

Accepted Answer

log218

Answer

log₂2 = 1

Answer

log23

Answer

log29

Question 7

Expand

Accepted Answer

C

Answer

A

Answer

B

Answer

D

Question 8

Question 8.

Accepted Answer

B

Answer

A

Answer

C

Answer

D

Question 9

Condense

Accepted Answer

logxyz3

Answer

log(xy/z³)

Answer

logx+logy+logz³

Answer

logx³y³z³

Question 10

Expand

Accepted Answer

log₈x+log₈y+5log₈z

Answer

log₈x+log₈y+log₈z

Answer

5log₈x+5log₈y+5log₈z

Answer

log₈xy+5log₈z

Question 11

Write log_b(x/y) as two logs

Accepted Answer

log_bx-log_by

Answer

log_bx+log_by

Answer

log_bx*log_by

Answer

log_bx/log_by

Question 12

Evaluate log_b(b)

Accepted Answer

1

Answer

-1

Answer

0

Answer

b

Question 13

Rewrite log_b(xⁿ)

Accepted Answer

nlogbx

Answer

(log_bx)ⁿ

Answer

xnlogbx

Answer

log_b(xⁿ)

Question 14

log(10 - 4a) = log(-3a + 8)

Accepted Answer

2

Answer

-1

Answer

No Solution

Answer

-13/3

Question 15

log(- 4x - 6) - log(6) = log(64)

Accepted Answer

-195/2

Answer

-14/3

Answer

-2

Answer

No Solution

Question 16

log(5) + log(8-5x) = 1

Accepted Answer

6/5

Answer

-195/3

Answer

-7/3

Answer

4

Question 17

Expand.

Accepted Answer

1/3 log x + 1/3 log y + 1/3 log z

Answer

1/3 log x + log y + log z

Answer

1/3 log x - 1/3 log y - 1/3 log z

Answer

3 log x + 3 log y + 3 log z

Question 18

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

Accepted Answer

log (12x²)

Answer

log (12 + 2x)

Answer

log (14x)

Answer

log (12 * 2x)

Question 19

Condense: log₂6+log₂3=

Accepted Answer

log218

Answer

log₂2 = 1

Answer

log23

Answer

log29

Question 20

Write log_b(xy) as two logs

Accepted Answer

log_bx+log_by

Answer

log_bx-log_by

Answer

log_bx*log_by

Answer

log_bx/log_by

Question 21

Expand

Accepted Answer

C

Answer

A

Answer

B

Answer

D

Question 22

Condense

Accepted Answer

logxyz3

Answer

log(xy/z³)

Answer

logx+logy+logz³

Answer

logx³y³z³

Question 23

Expand log₃(9x²)

Accepted Answer

2+2log3x

Answer

3+2log3x

Answer

log₃9+2log₃x

Answer

log9+2logx

Question 24

Rewrite 3⁴ = 81 in logarithmic form.

Accepted Answer

log₃81 = 4

Answer

log₃4 = 81

Answer

log₈₁3 = 4

Answer

log₄81 = 3

Question 25

Simplify 8^log₈x

Accepted Answer

x

Answer

0

Answer

1

Answer

8

Question 26

Simplify e^ln(x)

Accepted Answer

x

Answer

0

Answer

1

Answer

8

Question 27

Simplify 7^log₇(2x)

Accepted Answer

2x

Answer

0

Answer

2

Answer

1

Question 28

Condense

Accepted Answer

B

Answer

A

Answer

C

Answer

D

Question 29

Expand

Accepted Answer

C

Answer

A

Answer

B

Answer

D

Question 30

Condense

Accepted Answer

D

Answer

A

Answer

B

Answer

C

Question 31

Expand

Accepted Answer

B

Answer

A

Answer

C

Answer

D

Question 32

Condense

Accepted Answer

log₈(x⁶/y³)

Answer

log₈(x⁶)/log₈(y³)

Answer

log₈(x/y³)

Answer

log₈(x⁶y³)

Question 33

Write the following equation in exponential form:
log₂32 = 5

Accepted Answer

25 = 32

Answer

232 = 5

Answer

52 = 32

Answer

322 = 5

Question 34

Rewrite 3⁴ = 81 in logarithmic form.

Accepted Answer

log₃81 = 4

Answer

log₃4 = 81

Answer

log₈₁3 = 4

Answer

log₄81 = 3

Question 35

6x+2 = 18

Accepted Answer

-0.3869

Answer

0.3869

Answer

1.3869

Answer

-1.7594

Question 36

Solve:
6^{2x + 1}= 5^x

Accepted Answer

x = -.9076

Answer

x = -1

Answer

x = -.0509

Answer

x = -2.4702

Question 37

Evaluate log_b(1)

Accepted Answer

0

Answer

1

Answer

-1

Answer

b

Question 38

Evaluate b^log_b(x)

Accepted Answer

x

Answer

b

Answer

1

Answer

0

Question 39

Rewrite log_b(a) with base a

Accepted Answer

1/(logab)

Answer

-logba

Answer

1/(logba)

Answer

-logab

Question 40

log_bx=y iff _______

Accepted Answer

by=x

Answer

logby=x

Answer

bx=y

Answer

logxb=y

Question 41

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

Accepted Answer

log5162

Answer

log569

Answer

log556

Answer

log598

Question 42

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

Accepted Answer

log (12x²)

Answer

log (12 + 2x)

Answer

log (14x)

Answer

log (12 * 2x)

Question 43

Use a property of logs to write this in another way.
x log₇ y

Accepted Answer

log7 yx

Answer

log yx

Answer

log7 yx

Answer

log7 xy

Question 44

Write log_b(xy) as two logs

Accepted Answer

log_bx+log_by

Answer

log_bx-log_by

Answer

log_bx*log_by

Answer

log_bx/log_by

Question 45

Simplify log₄4^3x

Accepted Answer

3x

Answer

3

Answer

4

Answer

43x

Question 46

Expand log₆(5x³/y).

Accepted Answer

log₆5+3log₆x-log₆y

Answer

log₆5x³-log₆y

Answer

log₆5+log₆x³-log₆y

Question 47

Question 47.

Accepted Answer

log₈(x) + log₈(y) + 6log₈(z)

Answer

6log₈(xyz)

Answer

log₈(x) - log₈(y) - 6log₈(z)

Answer

log₈(x) + log₈(y) - log₈(z)

Question 48

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

Accepted Answer

log (12x²)

Answer

log (12 + 2x)

Answer

log (14x)

Answer

log (12 * 2x)

Question 49

Evaluate b^log_b(x)

Accepted Answer

x

Answer

b

Answer

1

Answer

0

Question 50

Condense

Accepted Answer

D

Answer

A

Answer

B

Answer

C

Question 51

Condense

Accepted Answer

logxyz3

Answer

log(xy/z³)

Answer

logx+logy+logz³

Answer

logx³y³z³

Question 52

Expand

Accepted Answer

6log₈u-2log₈v

Answer

6log₈v-2log₈u

Answer

3log₈u-2log₈v

Answer

6log₈u+2log₈v

Question 53

Write as one logarithm. Simplify, if possible.
log₃9 + log₃27

Accepted Answer

5

Answer

-1

Answer

4

Answer

1

Question 54

Write as one logarithm. Simplify, if possible.
log₆3 + log₆2

Accepted Answer

1

Answer

0

Answer

log65

Answer

log61

Question 55

Write as one logarithm. Simplify, if possible.
log₅125 - log₅25

Accepted Answer

1

Answer

0

Answer

5

Answer

-1

Question 56

Evaluate.
3 log₂4

Accepted Answer

6

Answer

3

Answer

2

Answer

4

Question 57

log(10R)

Accepted Answer

R

Answer

10

Answer

1

Answer

10R

Question 58

Evaluate.
log₆(¹/₂₁₆)

Accepted Answer

-3

Answer

3

Answer

1/3

Answer

-1/3

Question 59

Solve for x:
log₄ x = 3

Accepted Answer

64

Answer

4

Answer

12

Answer

32

Question 60

Condense, then simplify if possible.
log 6 - log 3 + 2 log 7

Accepted Answer

log 98

Answer

log 78

Answer

log 56

Answer

log 45

Question 61

Use the change of base formula and your calculator to approximate the log.

Accepted Answer

A

Answer

B

Answer

C

Answer

D

Question 62

Logarithms are the inverse of ___________.

Accepted Answer

Exponential

Answer

Trees

Answer

Quadratics

Answer

Square

Question 63

12 log u + 3 log v

Accepted Answer

log(v³u¹²)

Answer

log(vuw⁴)

Answer

log(u³/v¹²)

Question 64

24 log₄3-6log₄8

Accepted Answer

log₄(3²⁴/8⁶)

Answer

log₄(3⁴/8)

Answer

log₄(8⁶*3²⁴)

Evaluating Logarithms with Properties

72 questions

Write the following equation in exponential form:
log₂32 = 5

log₂(x + 5) = 3

log₂(x + 2) + log₂x = 3

4^(x-2)= 64^(x+1)

Write log_b(xy) as two logs

Condense: log₂6+log₂3=

Expand

Condense

Expand

Create a free account and access millions of resources

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

Evaluating Logarithms with Properties

72 questions

Write the following equation in exponential form:log232 = 5

log2(x + 5) = 3

log2(x + 2) + log2x = 3

4(x-2)= 64(x+1)

Write logb(xy) as two logs

Condense: log26+log23=

Expand

Condense

Expand

Create a free account and access millions of resources

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

Write the following equation in exponential form:
log₂32 = 5

log₂(x + 5) = 3

log₂(x + 2) + log₂x = 3

4^(x-2)= 64^(x+1)

Write log_b(xy) as two logs

Condense: log₂6+log₂3=