Quiz about Basic Logarithm 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)

Basic Logarithm Properties

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