Chapter 5.4, Problem 133AE

The Richter Scale Problems 133 and 134 on the next page use the following discussion: The Richter Scale is one way of converting 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 $M(x)$, given by

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

where $x_0={10}^{-3}$ 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 Mexico City in 1985: seismographic reading of 125,892 millimeters 100 kilometers from the center.