AnswersFL-1200330-Algebra 2 CREvaluating Logarithmic ExpressionsQuestion 18
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Evaluating Logarithmic Expressions

Question 18 • FL-1200330-Algebra 2 CR

Which did you include in your answer?

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

Explanation

The Richter scale is logarithmic: each increase of 1 corresponds to 10 times the measured intensity. From magnitude 5 to magnitude 8 is an increase of 3 units, so the intensity ratio is 10³ = 1,000. Equivalently, the two magnitudes correspond to 10⁵ and 10⁸ relative to the standard, and 10⁸ ÷ 10⁵ = 10³. Thus all three statements correctly describe the comparison.

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