Question

the magnitude, m, of an earthquake is defined to be m = log(\frac{i}{s}), where i is the intensity of the earthquake (measured by the amplitude of the seismograph wave) and s is the intensity of a \standard\ earthquake, which is barely detectable. which equation represents the magnitude of an earthquake that is 10 times more intense than a standard earthquake?
m = log(\frac{i}{10s})
m = log(10s)
m = log(\frac{10s}{s})
m = log(\frac{10}{s})

Explanation:

Step1: Identify the given formula

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

Step2: Find the new intensity

If an earthquake is 10 times more intense than a standard earthquake, then the new intensity $I_{new}=10S$.

Step3: Substitute the new - intensity into the magnitude formula

Substitute $I = 10S$ into $M=\log\frac{I}{S}$. We get $M=\log\frac{10S}{S}$.

Step4: Simplify the expression

Since $\frac{10S}{S}=10$, the magnitude formula becomes $M = \log 10$. But if we start from the general substitution, the magnitude formula for the earthquake with intensity $10S$ is $M=\log\frac{10S}{S}$.

Answer:

C. $M=\log\frac{10S}{S}$