how many more times intense is an earthquake that measures 8 on the richter scale than an earthquake that…

Explanation:

Step1: Recall Richter - scale formula

The intensity $I$ of an earthquake is related to the Richter - scale magnitude $M$ by the formula $M=\log_{10}\left(\frac{I}{I_0}\right)$, where $I_0$ is a reference intensity. For an earthquake of magnitude $M_1$, we have $M_1 = \log_{10}\left(\frac{I_1}{I_0}\right)$, so $I_1 = I_0\times10^{M_1}$. Similarly, for an earthquake of magnitude $M_2$, $I_2 = I_0\times10^{M_2}$.

Step2: Find the ratio of intensities

We want to find the ratio $\frac{I_1}{I_2}$, where $M_1 = 8$ and $M_2 = 5$. Substitute the expressions for $I_1$ and $I_2$ into the ratio: $\frac{I_1}{I_2}=\frac{I_0\times10^{M_1}}{I_0\times10^{M_2}}$. The $I_0$ terms cancel out, and we get $\frac{I_1}{I_2}=10^{M_1 - M_2}$.

Step3: Calculate the ratio

Substitute $M_1 = 8$ and $M_2 = 5$ into the formula $\frac{I_1}{I_2}=10^{M_1 - M_2}$. Then $M_1 - M_2=8 - 5 = 3$, and $\frac{I_1}{I_2}=10^{3}=1000$.

Answer:

An earthquake that measures 8 on the Richter - scale is 1000 times more intense than an earthquake that measures 5.