The magnitude of earthquake 1 is 5.6. If earthquake 2 is 81.28 times as intense as earth- quake 1, find the magnitude of earthquake 2. Round your answer to 1 decimal place.
A) 7.5
B) 3.7
C) 86.9
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 earthquakes, and $M_2$ and $M_1$ are their magnitudes. Given that earthquake 2 is 81.28 times as intense as earthquake 1, we have $I_2/I_1 = 81.28$. Taking the logarithm (base 10) of both sides gives $\log(81.28) = M_2 - 5.6$. Since $\log(81.28) \approx 1.91$, we find $M_2 = 1.91 + 5.6 = 7.51$, which rounds to 7.5.

The Magnitude of Earthquake 1 Is 5