Question about logarithm and earthquake

The formula used to find the measure of the magnitude of an earthquake is:


(x represents the seismographic reading in millimeters ,x0 represents   a zero-level earthquake the same distance from the epicenter)


Q:

 

Suppose that you wanted to find the magnitude of the San Francisco Earthquake of 1906 given the data that a seismographic reading of 7,943 millimeters was registered 100 kilometers from the center.

 

First, we will need to use the logarithmic models formula for finding magnitude of an earthquake:

 

 

In the formula, we substitute 7943 mm for the value of x, and 0.001 for the value of x_o:

 

 

Now, we type into a calculator to evaluate the function and find M(x):

 

 

Therefore, the magnitude of the earthquake that hit San Francisco in 1906 was 6.9.