The magnitude of earthquake 1 is 5.8. If earthquake 2 is 39.81 times as intense as earth- quake 1, find the magnitude of earthquake 2. Round your answer to 1 decimal place.
A) 7.4
B) 4.2
C) 45.6
D) 8.2

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 two earthquakes, and $M_2$ and $M_1$ are their magnitudes. Given that earthquake 2 is 39.81 times as intense as earthquake 1, we have $I_2/I_1 = 39.81$. Taking the logarithm (base 10) of both sides gives $\log(39.81) = M_2 - 5.8$. Since $\log(39.81) \approx 1.6$, we find $M_2 = 1.6 + 5.8 = 7.4$.

The Magnitude of Earthquake 1 Is 5