Chapter 6.4, Problem 134AE

The Richter Scale Problems 133 and 134 on the next page use the following discussion: The Richter scale is one way of concerting seismographic readings into numbers that provide an easy reference for measuring the magnitude M of an earthquake. All earthquakes are compared to a zero-level earthquake whose seismographic reading measures $0.001$ millimeter at a distance of 100 kilometers from the epicenter. An earthquake whose seismographic reading measures $x$ millimeters has magnitude $M\left(x\right)$, given by

$M\left(x\right)\text{ = log}\left(\frac{x}{x_0}\right)$

where $x_0{\text{ = 10}}^{-3}$ is the reading of a zero-level earthquake the same distance from its epicenter. In Problems 133 and 134, determine the magnitude of each earthquake.

Magnitude of an Earthquake San Francisco in1906: seismographic reading of 50,119 millimeters 100 kilometers from the center