Chapter 5.4, Problem 131AYU

To determine

Magnitude of an earthquake in Mexico City in 1985, where seismographic reading of 125,892 millimetres 100 kilometres from the centre.

Answer to Problem 131AYU

Solution:

The magnitude of earthquake is $8.1$

Explanation of Solution

Given Information:

An earthquake whose seismographic reading measures $x$ millimetres has magnitude $M(x)$ given by $M(x)=\log \left(\frac{x}{x_0}\right)$, where $x_0={10}^{-3}$ is the reading of a zero-level earthquake the same distance from its epicentre.

Explanation:

An earthquake whose seismographic reading measures $x$ millimetres has magnitude $M(x)$ given by $M(x)=\log \left(\frac{x}{x_0}\right)$, where $x_0={10}^{-3}$ is the reading of a zero-level earthquake the same distance from its epicentre.

Therefore, $M(x)=\log \left(\frac{x}{{10}^{-3}}\right)$

The seismographic reading of Mexico City in 1985 is 125,892 millimetres 100 kilometres from the centre.

Substituting $x=125892$ in $M(x)=\log \left(\frac{x}{{10}^{-3}}\right)$

$\Rightarrow M(x)=\log \left(\frac{125892}{{10}^{-3}}\right)$

$M(x)=\log \left(125892000\right)$

$M(x)=8.1$.

Thus, the magnitude of the earthquake is $8.1$.