Question

In $2014$, Chile experienced an intense earthquake with a magnitude of $8.2$on the Richter scale. In $2014$, Los Angeles also experienced an earthquake which measured $5.1$on the Richter scale. Compare the intensities of the

two earthquakes.

Short answer

The intensity of the $2014$earthquake in Chile was about $1258.9$times the intensity of the $2014$ earthquake in Los Angeles.

Step-by-step solution

Step 1. Given information.

The given magnitudes are $8.2$and $5.1$.

The magnitudeR of an earthquake is measured by

$R=\log \left(I\right)$

whereI is the intensity of its shock wave.

Step 2. Comparing the intensities.

First, convert the given magnitudes into

intensities.

$$\begin{gathered} R=\log \left(I\right) \\ 8.2=\log \left(I\right) \\ I={10}^{8.2} \end{gathered}$$

Similarly

$$\begin{gathered} R=\log \left(I\right) \\ 5.1=\log \left(I\right) \\ I={10}^{5.1} \end{gathered}$$

Now comparing the intensities

$$\begin{gathered} \frac{{10}^{8.2}}{{10}^{5.1}}={10}^{8.2-5.1} \\ ={10}^{3.1} \\ =1258.9 \end{gathered}$$

The intensity of the $2014$earthquake in Chile was about $1258.9$ times the intensity of the $2014$ earthquake in Los Angeles.