what is the intensity of an earthquake with a magnitude of 3?\n3 times a standard earthquake\n100 times a…

Explanation:

Step1: Recall magnitude - intensity formula

The magnitude $M$ of an earthquake is related to the intensity $I$ by the formula $M=\log_{10}\left(\frac{I}{I_0}\right)$, where $I_0$ is the intensity of a standard earthquake. Given $M = 3$, we can rewrite the formula as $3=\log_{10}\left(\frac{I}{I_0}\right)$.

Step2: Convert logarithmic to exponential form

By the definition of logarithms, if $\log_{a}b = c$, then $b=a^{c}$. So, from $3=\log_{10}\left(\frac{I}{I_0}\right)$, we get $\frac{I}{I_0}=10^{3}$.

Step3: Solve for $I$

Multiply both sides of the equation $\frac{I}{I_0}=10^{3}$ by $I_0$ to find $I = 1000I_0$.

Answer:

C. 1,000 times a standard earthquake