Deck 20: Logarithmic Functions

Question 1

The magnitude of earthquake 1 is 4.5, and the magnitude of earthquake 2 is 6.5.How do their intensities compare? ​

A) Earthquake 1 is 100 times as intense as earthquake 2.
B) Earthquake 1 is 2 times as intense as earthquake 2.
C) Earthquake 2 is 2 times as intense as earthquake 1.
D) Earthquake 2 is 100 times as intense as earthquake 1.

Answer 1

Earthquake 2 is 100 times as intense as earthquake 1.

Question 2

If is 7.01, then the value of is (rounded to two decimal places if necessary) ​

A) 20.75
B) 9.97
C) 21.43
D) 10.14

Answer 2

9.97

Question 3

The inverse of a logarithm is an exponential function.

Answer 3

True

Question 4

The Richter scale is a logarithmic scale.

Question 5

The magnitude of earthquake 1 is 8.6.Earthquake 2 is half as intense as earthquake 1.What is the magnitude of earthquake 2? Round your answer to 1 decimal place. ​

A) 7.7
B) 8.3
C) 4.3
D) 5.1

Question 6

If is 3.51, then the value of is ​

A) 10.53
B) 10.97
C) 6.51
D) 7.18

Question 7

The magnitude M of an earthquake depends on the relative intensity I of the quake.The relationship is . ​
Express the relative intensity as a function of the magnitude.
​

A)
B)
C)
D)

Question 8

Multiplying x by adds t to .

Question 9

If is 4.19, then the value of is (rounded to two decimal places if necessary) ​

A) 9.3
B) 7.35
C) 9.91
D) 6.41

Question 10

The crossing graphs method is not useful for solving equations involving logarithms.

Question 11

The magnitude of earthquake 1 is 4.7, and the magnitude of earthquake 2 is 8.How do their intensities compare? ​

A) Earthquake 1 is 1,995.26 times as intense as earthquake 2.
B) Earthquake 1 is 3.3 times as intense as earthquake 2.
C) Earthquake 2 is 3.3 times as intense as earthquake 1.
D) Earthquake 2 is 1,995.26 times as intense as earthquake 1.

Question 12

The magnitude of earthquake 1 is 5.5.If earthquake 2 is 1,000 times as intense as earthquake 1, then the magnitude of earthquake 2 is (rounded to one decimal place if necessary) ​

A) 8.5
B) 2.5
C) 1,005.5
D) 5,500

Question 13

The graph of the logarithm is concave down.

Question 14

The logarithm is the inverse of an exponential function.

Question 15

The magnitude scale for brightness of stars is a logarithmic scale.

Question 16

The graph of the logarithm has a point of inflection.

Question 17

If is 8.45, then the value of is ​

A) 0.24
B) 6.45
C) 0.44
D) 7.01

Question 18

The magnitude of earthquake 1 is 5.4.If earthquake 2 is 14.13 times as intense as earthquake 1, find the magnitude of earthquake 2.Round your answer to 1 decimal place. ​

A) 6.6
B) 4.3
C) 19.5
D) 7.3

Question 19

The decibel scale is a logarithmic scale.

Question 20

The logarithm function is always less than 100.

Question 21

We use ln to denote the natural logarithm.The solution for t of the equation is: ​

A)
B)
C)
D)

Question 22

The solution for t of the equation is: ​

A)
B)
C)
D)

Question 23

The inverse of is ​

A)
B)
C)
D)

Question 24

The inverse of is ​

A)
B)
C)
D)

Question 25

The inverse of is ​

A)
B)
C)
D)

Question 26

The magnitude of a star is a measure of its brightness, and it is related to the relative intensity of light reaching Earth from the star.The relationship is Magnitude Relative intensity).
If relative intensity is divided by 100, how is magnitude affected?
​

A) Magnitude is decreased by 2.
B) Magnitude is increased by 5.
C) Magnitude is increased by 2.
D) Magnitude is decreased by 5.

Question 27

The solution for ​t of the equation ​ is:
​

A)
B)
C)
D)

Question 28

The decibel, a measure of loudness, is related to the relative intensity of sound by the formula Decibels Relative intensity).
If relative intensity is multiplied by 104.71, how are decibels affected?
​

A) Decibels are increased by 20.2.
B) Decibels are decreased by 2.02.
C) Decibels are increased by 2.02.
D) Decibels are decreased by 20.2.

Question 29

The decibel, a measure of loudness, is related to the relative intensity of sound by the formula Decibels (Relative intensity).
If relative intensity is divided by 1,000, how are decibels affected?
​

A) Decibels are increased by 3.
B) Decibels are decreased by 3.
C) Decibels are increased by 30.
D) Decibels are decreased by 30.

Question 30

We use ln to denote the natural logarithm.What is the value of ? Round your answer to two decimal places if necessary. ​

A) 6
B) 2.61
C) 403.43
D) 2.82

Question 31

The graph of is ​

A) ​
B) ​
C) ​
D) ​

Question 32

The graph of the logarithm is ​

A) Decreasing and concave down.
B) Decreasing and concave up.
C) Increasing and concave up.
D) Increasing and concave down.

Question 33

We use ln to denote the natural logarithm.What is the value of ? ​

A) 5.92
B) 2.57
C) 372.41
D) 2.65

Question 34

The magnitude of a star is a measure of its brightness, and it is related to the relative intensity of light reaching Earth from the star.The relationship is Magnitude (Relative intensity).
If relative intensity is multiplied by 123.03.how is magnitude affected? Round your answer to two decimal places if necessary.
​

A) Magnitude is decreased by 2.09.
B) Magnitude is increased by 5.23.
C) Magnitude is increased by 2.09.
D) Magnitude is decreased by 5.23.

Question 35

The decibel, a measure of loudness, is related to the relative intensity of sound by the formula Decibels (Relative intensity).
If relative intensity is multiplied by 1,000, how are decibels affected?
​

A) Decibels are increased by 3.
B) Decibels are decreased by 3.
C) Decibels are increased by 30.
D) Decibels are decreased by 30.

Question 36

We use ln to denote the natural logarithm.The solution for t of the equation is: ​

A)
B)
C)
D)

Question 37

The magnitude of a star is a measure of its brightness, and it is related to the relative intensity of light reaching Earth from the star.The relationship is Magnitude (Relative intensity).
If relative intensity is multiplied by 100, how is magnitude affected?
​

A) Magnitude is decreased by 2.
B) Magnitude is increased by 5.
C) Magnitude is increased by 2.
D) Magnitude is decreased by 5.

Question 38

The magnitude M of a star is a measure of its brightness, and it is related to the relative intensity I of light reaching Earth from the star.The relationship is . Express relative intensity as a function of magnitude.
​

A)
B)
C)
D)

Question 39

The decibel level D, a measure of loudness, is related to the relative intensity I of sound by the formula . ​
Express relative intensity as a function of decibels.
​

A)
B)
C)
D)

Question 40

The decibel, a measure of loudness, is related to the relative intensity of sound by the formula Decibels (Relative intensity).
A whisper in a library is about 34 decibels.What decibel level is produced by 12 people whispering in the library? Round your answer to the nearest whole number.
​

A) 408 decibels
B) 45 decibels
C) 410 decibels
D) 47 decibels

Question 41

The inverse of is ​

A)
B)
C)
D)