Chapter 6.4, Problem 134AYU

To determine

To find: The Richter Scale: 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 $M\left(x\right)$, given by

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

Where $x_0={10}^{-3}$ is the reading of a zero-level earthquake the same distance from its epicenter., determine the magnitude for the following earthquake,

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