Question

R=log( I/Io) where Io is the intensity of a certain very small earthquake. What is the magnitude of an earthquake with intensity 8000 times Io?

Answer 1

\[I = 8000 I_{0}\]\[R = \log \left( \frac{I}{I_0} \right) \]\[R = \log \left( \frac{8000I_0}{I_0} \right)\]\[R = \log \left( 8000\right) \]\[R = \log \left( 8 \right)+\log \left( 10^3 \right) \]\[R = 3 + \log \left( 8 \right)\]\[R \approx 3.9\]