The magnitude of earthquake 1 is 4.6. If earthquake 2 is 12.59 times as intense as earth- quake 1, find the magnitude of earthquake 2. Round your answer to 1 decimal place.
A) 5.7
B) 3.5
C) 17.2
D) 6.1

Question

Quizplus · Accepted Answer

The magnitude of an earthquake is measured on a logarithmic scale. The formula to compare the magnitudes of two earthquakes when their intensities are known is $M_2 = M_1 + \log_{10}(I_2/I_1)$, where $M_1$ and $M_2$ are the magnitudes of the earthquakes, and $I_2/I_1$ is the ratio of their intensities. Given $M_1 = 4.6$ and $I_2/I_1 = 12.59$, we find $M_2 = 4.6 + \log_{10}(12.59) \approx 4.6 + 1.1 = 5.7$.

The Magnitude of Earthquake 1 Is 4