Evaluating Logarithmic Expressions

Question 1

⇒ 0

Revolt · Accepted Answer

1

Question 2

An earthquake with a magnitude of about 2.0 or less is called a microearthquake. It is not usually felt. The intensity of an earthquake with a magnitude of 2 is how many times greater than the intensity of an a standard earthquake?

Revolt · Accepted Answer

C: 100 times greater

Question 3

By what factor does the intensity increase for each whole-number increase in the Richter scale? Use your understanding of logarithms and the inverse relationship between logarithms and exponents to explain your answer.

Revolt · Accepted Answer

The intensity of an earthquake increases by a factor of 10 for each whole-number increase on the Richter scale. This is because the Richter scale is based on common logarithms (base 10). According to the inverse relationship between logarithms and exponents, an increase of 1 in magnitude corresponds to an intensity increase of 10^1. For example, a magnitude 3 earthquake is 10^3 times more intense than a standard earthquake, while a magnitude 2 earthquake is 10^2 times more intense; since 10^3 = 10^2 × 10, the intensity is 10 times greater.

Question 4

How many more times intense is an earthquake that measures 8 on the Richter scale than an earthquake that measures 5? Explain your answer.

Revolt · Accepted Answer

A magnitude 8 earthquake is 1,000 times more intense than a magnitude 5 earthquake. This is because each unit on the Richter scale represents a 10-fold increase in intensity. Since the difference between 8 and 5 is 3 units, the intensity difference is 10 to the power of 3 (10^3), which equals 1,000.

Question 5

In 2010, Haiti was hit by a devastating earthquake, which registered at 7.0 on the Richter scale. The largest recorded earthquake since 1900 occurred in 1960 in Valdivia, Chile, and registered at 9.5 on the Richter scale. About how many times greater was the intensity of the Chilean earthquake?

Revolt · Accepted Answer

D: 316

Question 6

What is the magnitude of an earthquake that is 10,000 times more intense than a standard earthquake?M =

Revolt · Accepted Answer

4

Question 7

Which equation represents the magnitude of an earthquake that is 100 times more intense than a standard earthquake?

Revolt · Accepted Answer

B: ; C:

Question 8

What is the intensity of an earthquake with a magnitude of 3?

Revolt · Accepted Answer

C: 1,000 times a standard earthquake

Question 9

Which did you include in your answer?

Revolt · Accepted Answer

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Question 10

Which did you include in your answer?

Revolt · Accepted Answer

A: A magnitude 8 earthquake is 1,000 times more intense than a magnitude 5 earthquake.; B: A magnitude 8 earthquake is 108 times more intense than a standard earthquake, while a magnitude 5 earthquake is 105 times more intense than a standard earthquake, and 108 ÷ 105 = 103.; C: Each unit increase on the Richter scale corresponds to an intensity increase by a factor of 10. So from 5 to 8 on the Richter scale, the intensity increases by 103 = 1,000

Evaluating Logarithmic Expressions Answers

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Evaluating Logarithmic Expressions Answers

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