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(100s) the magnitude is m =

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. If an earthquake has an intensity $I$ that is 100 times more intense than the standard earthquake, then $I = 100S$.

Step2: Substitute $I = 100S$ into the formula

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

Step3: Simplify the expression

Since $\frac{100S}{S}=100$, then $M = \log(100)$. And since $100 = 10^{2}$, by the property of logarithms $\log(a^{b})=b\log(a)$ (with base - 10 here), $\log(100)=\log(10^{2}) = 2$.

Answer:

2