Chapter 4.4, Problem 134AYU

The Richter Scale Problems $133$ and $134$ 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 epicentre. An earthquake whose seismographic reading measures $x$ milimeters has magnitude $M\left(x\right)$, given by

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

Where $x_0={10}^{-3}$ is the reading of a zero-level earthquake the same distance from its epicenter. In Problems $113$ and $134$, determine the magnitude of each earthquake.

Magnitude of an Earthquake San Francisco in $1906$: seismographic reading of $50,119$ millimeters $100$ kilometers from the center.