AnswersFL-1200330-Algebra 2 CREvaluating Logarithmic Expressions

Evaluating Logarithmic Expressions Answers

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1
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What is the value of ?

Question illustration
A
2
B
3
C
4
D
5
2
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Which equation has x = –6 as the solution?

A
log Subscript x Baseline 36 = 2
Option A
B
log Subscript 3 Baseline (2 x minus 9) = 3
Option B
C
log Subscript 3 Baseline 216 = x
Option C
D
log Subscript 3 Baseline (negative 2 x minus 3) = 2
Option D
3

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
4

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?

Question illustration
A
M = log StartFraction I Over S EndFraction
Option A
B
M = log (10 S)
Option B
C
M = log StartFraction 10 S Over S EndFraction
Option C
D
M = log StartFraction 10 Over S EndFraction
Option D
5

Which equation is equivalent to ?

Question illustration
A
3 squared = left-bracket log Subscript 3 Baseline (x + 5) right-bracket cubed
Option A
B
2 cubed = left-bracket log Subscript 3 Baseline (x + 5) right-bracket squared
Option B
C
3 squared = x + 5
Option C
D
2 cubed = x + 5
Option D
6

What is the value of log 43? Use the calculator. Round your answer to the nearest tenth.

A
0.6
B
1.6
C
3.8
D
4.7
7

Which equation is equivalent to ?

Question illustration
A
2 Superscript x Baseline = 36
Option A
B
x squared = 36
Option B
C
36 Superscript x Baseline = 2
Option C
D
x squared = 36 squared
Option D
8

Which logarithmic equation is equivalent to 32 = 9?

A
2 = log Subscript 3 Baseline 9
Option A
B
2 = log Subscript 9 Baseline 3
Option B
C
3 = log Subscript 2 Baseline 9
Option C
D
3 = log Subscript 9 Baseline 2
Option D
9

What is the solution of ?

Question illustration
A
4
B
5
C
15
D
20
10

What is the value of ?

Question illustration
A
Negative three-halves
Option A
B
Negative two-thirds
Option B
C
Two-thirds
Option C
D
Three-halves
Option D
11

What is the value of ?

Question illustration
A
–6
B
–2
C
2
D
6
12

Which equation is equivalent to ?

Question illustration
A
2 Superscript x Baseline = 36
Option A
B
x squared = 36
Option B
C
36 Superscript x Baseline = 2
Option C
D
x squared = 36 squared
Option D
13

Which equation is equivalent to ?

Question illustration
A
3 squared = left-bracket log Subscript 3 Baseline (x + 5) right-bracket cubed
Option A
B
2 cubed = left-bracket log Subscript 3 Baseline (x + 5) right-bracket squared
Option B
C
3 squared = x + 5
Option C
D
2 cubed = x + 5
Option D
14

Which logarithmic equation is equivalent to 82 = 64?

A
2 = log Subscript 6 Baseline 64
Option A
B
2 = log Subscript 64 Baseline 8
Option B
C
8 = log Subscript 2 Baseline 64
Option C
D
64 = log Subscript 2 Baseline 8
Option D
15

What is the value of ?

Question illustration
A
Negative three-halves
Option A
B
Negative two-thirds
Option B
C
Two-thirds
Option C
D
Three-halves
Option D
16

What is the value of ?

Question illustration
A
–3
B
Negative one-third
Option B
C
One-third
Option C
D
3
17

What is the value of ?

Question illustration
A
1
B
2
C
4
D
8
18

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
19

Which equation has x = –6 as the solution?

A
log Subscript x Baseline 36 = 2
Option A
B
log Subscript 3 Baseline (2 x minus 9) = 3
Option B
C
log Subscript 3 Baseline 216 = x
Option C
D
log Subscript 3 Baseline (negative 2 x minus 3) = 2
Option D
20

What is the value of ?

Question illustration
A
2
B
3
C
4
D
5

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