Evaluating Logarithmic Expressions Answers
Which equation represents the magnitude of an earthquake that is 100 times more intense than a standard earthquake?
What is the intensity of an earthquake with a magnitude of 3?
M = log S S = [___]
1
The magnitude is M =
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?
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.
The intensity increases by a factor of 10 for each whole-number increase in the Richter scale because the scale uses base-10 logarithms. Increasing the magnitude by 1 multiplies the intensity by 10.
Which did you include in your answer?
How many more times intense is an earthquake that measures 8 on the Richter scale than an earthquake that measures 5? Explain your answer.
A magnitude 8 earthquake is 1,000 times more intense than a magnitude 5 earthquake because 10^(8-5) = 10^3 = 1,000.
Which did you include in your answer?
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