The magnitude on the Richter scale of an earthquake as a function of its intensity I is given by \(M = \log_{10}\left( \frac{I}{I_{0}} \right),\)

where \( I_{0}\) is some fixed reference level of intensity.

The 1906 San Francisco earthquake had a magnitude of 8.3 on the Richter scale. Suppose that at the same time in South America there was an earthquake with magnitude 4 that caused only minor damage. How many times more intense was the San Francisco earthquake than the South American one?

Hint: You don't need to know what \(I_{0}\) is. Plug in the respective magnitudes and use the log properties you know to compare the resulting values for \(I\) in terms of this \(I_{0} \).

Sloan
Jun 7, 2018