Question

the magnitude, m, of an earthquake is defined to be m = log(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(i/10s)
m = log(10s)
m = log(10s/s)
m = log(10/s)

Explanation:

Step1: Identify the given intensity

The intensity of a standard earthquake is $S$. The earthquake in question is 10 times more intense than a standard earthquake, so its intensity $I = 10S$.

Step2: Substitute into the magnitude - formula

The magnitude formula is $M=\log\frac{I}{S}$. Substitute $I = 10S$ into the formula: $M=\log\frac{10S}{S}$.

Step3: Simplify the fraction

$\frac{10S}{S}=10$, so $M = \log10$.

Answer:

$M=\log\frac{10S}{S}$ (the third option)