The magnitude of earthquake 1 is 5.9. If earthquake 2 is 13.49 times as intense as earth- quake 1, find the magnitude of earthquake 2. Round your answer to 1 decimal place.
A) 7
B) 4.8
C) 19.4
D) 8

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 given by $\log(I_2/I_1) = M_2 - M_1$, where $I_2$ and $I_1$ are the intensities of the earthquakes and $M_2$ and $M_1$ are their magnitudes, respectively. Given that earthquake 2 is 13.49 times as intense as earthquake 1, we can set $I_2/I_1 = 13.49$. Taking the logarithm (base 10) of both sides gives $\log(13.49) = M_2 - 5.9$. Solving for $M_2$, we find that $M_2 = \log(13.49) + 5.9$. Since $\log(13.49) \approx 1.13$, $M_2 \approx 1.13 + 5.9 = 7.03$, which rounds to 7.0.

The Magnitude of Earthquake 1 Is 5