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 new intensity

If the earthquake is 10 times more intense than a standard earthquake, then $I = 10S$.

Step2: Substitute into the magnitude formula

The magnitude formula is $M=\log\frac{I}{S}$. Substituting $I = 10S$ into it, we get $M=\log\frac{10S}{S}$.

Step3: Simplify the fraction

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

Answer:

$M=\log\frac{10S}{S}$ (corresponding to the third - option in the multiple - choice list)