Question

In $1906$, San Francisco experienced an intense earthquake with a magnitude of $7.8$on the Richter scale. In $1989$, the Loma Prieta earthquake also affected the San Francisco area and measured $6.9$on the Richter scale. Compare the intensities of the two earthquakes.

Short answer

The intensity of the $1906$earthquake was about $7.9$times the intensity of the $1989$earthquake.

Step-by-step solution

Step 1. Given information.

The given magnitudes are $7.8$and $6.9$.

The magnitude R of an earthquake is measured by

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

where I is the intensity of its shock wave.

Step 2. Comparing the intensities.  

First, convert the given magnitudes into intensities.

$$\begin{gathered} R=\log \left(I\right) \\ 7.8=\log \left(I\right) \\ I={10}^{7.8} \end{gathered}$$

Similarly

$$\begin{gathered} R=\log \left(I\right) \\ 6.9=\log \left(I\right) \\ I={10}^{6.9} \end{gathered}$$

Now comparing the intensities

$$\begin{gathered} \frac{{10}^{7.8}}{{10}^{6.9}}={10}^{7.8-6.9} \\ ={10}^{0.9} \\ =7.9 \end{gathered}$$

Therefore, the intensity of the $1906$earthquake was about $7.9$times the intensity of the $1989$earthquake.