what is the magnitude of an earthquake that is 5,011 times more intense than a standard earthquake? round…

Explanation:

Step1: Recall magnitude - intensity formula

The formula for the magnitude $M$ of an earthquake in terms of its intensity $I$ relative to a standard intensity $I_0$ is $M=\log_{10}\left(\frac{I}{I_0}\right)$. We are given that $I = 5011I_0$.

Step2: Substitute the value of $I$ into the formula

Substitute $I = 5011I_0$ into the formula $M=\log_{10}\left(\frac{I}{I_0}\right)$. Then $M=\log_{10}\left(\frac{5011I_0}{I_0}\right)$. Since $\frac{5011I_0}{I_0}=5011$, we have $M = \log_{10}(5011)$.

Step3: Calculate the logarithm

Using a calculator, $\log_{10}(5011)\approx3.7$.

Answer:

$3.7$