Evaluating Logarithmic Expressions Answers…

1

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What is the value of ?

A

–6

B

–2

C

2

D

6

2

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What is the solution of ?

A

–18

B

–2

C

2

D

10

3

What is the solution of ?

A

4

B

5

C

15

D

20

4

Which equation has x = –6 as the solution?

A

log Subscript x Baseline 36 = 2

B

log Subscript 3 Baseline (2 x minus 9) = 3

C

log Subscript 3 Baseline 216 = x

D

log Subscript 3 Baseline (negative 2 x minus 3) = 2

5

Which logarithmic equation is equivalent to 32 = 9?

A

2 = log Subscript 3 Baseline 9

B

2 = log Subscript 9 Baseline 3

C

3 = log Subscript 2 Baseline 9

D

3 = log Subscript 9 Baseline 2

6

What is the value of ?

A

Negative three-halves

B

Negative two-thirds

C

Two-thirds

D

Three-halves

7

Which equation is equivalent to ?

A

2 Superscript x Baseline = 36

B

x squared = 36

C

36 Superscript x Baseline = 2

D

x squared = 36 squared

8

What is the value of log 13? Use a calculator. Round your answer to the nearest tenth.

A

0.1

B

0.3

C

1.1

D

2.6

9

Which logarithmic equation is equivalent to 82 = 64?

A

2 = log Subscript 6 Baseline 64

B

2 = log Subscript 64 Baseline 8

C

8 = log Subscript 2 Baseline 64

D

64 = log Subscript 2 Baseline 8

10

A Cepheid star is a type of variable star, which means its brightness is not constant. The relationship between the brightness of a Cepheid star and its period, or length of its pulse, is given by M = –2.78(log P) – 1.35, where M is the absolute magnitude, or brightness, of the star, and P is the number of days required for the star to complete one cycle. What is the absolute magnitude of a star that has a period of 45 days? Use a calculator. Round your answer to the nearest hundredth.

A

–5.95

B

–4.60

C

3.25

D

4.60

11

What is the value of log 13? Use a calculator. Round your answer to the nearest tenth.

A

0.1

B

0.3

C

1.1

D

2.6

12

What is the solution of ?

A

–18

B

–2

C

2

D

10

13

What is the value of ?

A

–3

B

Negative one-third

C

One-third

D

3

14

What is the value of ?

A

2

B

3

C

4

D

5

15

Which logarithmic equation is equivalent to 82 = 64?

A

2 = log Subscript 6 Baseline 64

B

2 = log Subscript 64 Baseline 8

C

8 = log Subscript 2 Baseline 64

D

64 = log Subscript 2 Baseline 8

16

The magnitude, M, of an earthquake is defined to be , where I is the intensity of the earthquake (measured by the amplitude of the seismograph wave) and S is the intensity of a “standard” earthquake, which is barely detectable. Which equation represents the magnitude of an earthquake that is 10 times more intense than a standard earthquake?

A

M = log StartFraction I Over S EndFraction

B

M = log (10 S)

C

M = log StartFraction 10 S Over S EndFraction

D

M = log StartFraction 10 Over S EndFraction

17

Which equation is equivalent to ?

A

3 squared = left-bracket log Subscript 3 Baseline (x + 5) right-bracket cubed

B

2 cubed = left-bracket log Subscript 3 Baseline (x + 5) right-bracket squared

C

3 squared = x + 5

D

2 cubed = x + 5

18

Which equation is equivalent to ?

A

2 Superscript x Baseline = 36

B

x squared = 36

C

36 Superscript x Baseline = 2

D

x squared = 36 squared

19

What is the value of ?

A

1

B

2

C

4

D

8

20

The magnitude, M, of an earthquake is defined to be , where I is the intensity of the earthquake (measured by the amplitude of the seismograph wave) and S is the intensity of a “standard” earthquake, which is barely detectable. Which equation represents the magnitude of an earthquake that is 10 times more intense than a standard earthquake?

A

M = log StartFraction I Over S EndFraction

B

M = log (10 S)

C

M = log StartFraction 10 S Over S EndFraction

D

M = log StartFraction 10 Over S EndFraction

Evaluating Logarithmic Expressions Answers

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