Question

which equation represents the magnitude of an earthquake that is 100 times more intense than a standard earthquake?
$m = \log\frac{i}{100s}$
$m = \log\frac{100s}{s}$
$m = \log(100s)$
$m = \log\frac{100}{s}$

Explanation:

Step1: Recall magnitude - intensity formula

The magnitude $M$ of an earthquake is given by the formula $M = \log\frac{I}{S}$, where $I$ is the intensity of the earthquake and $S$ is the intensity of a standard earthquake.

Step2: Identify the given intensity relation

We are given that the intensity of the earthquake $I$ is 100 times the intensity of a standard earthquake, so $I = 100S$.

Step3: Substitute into the magnitude formula

Substitute $I = 100S$ into $M=\log\frac{I}{S}$, we get $M=\log\frac{100S}{S}$.

Answer:

$M=\log\frac{100S}{S}$