the magnitude, m, of an earthquake is defined to be $m = \\log\\frac{i}{s}$, where i is the intensity of the…

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?\n$m = \\log\\frac{i}{10s}$\n$m = \\log(10s)$\n$m = \\log\\frac{10s}{s}$\n$m = \\log\\frac{10}{s}$

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?\n$m = \\log\\frac{i}{10s}$\n$m = \\log(10s)$\n$m = \\log\\frac{10s}{s}$\n$m = \\log\\frac{10}{s}$

Answer

Explanation:

Step1: Identify the given intensity relationship

Given that the intensity $I$ of the earthquake is 10 times the intensity of a standard earthquake $S$, so $I = 10S$.

Step2: Substitute into the magnitude - formula

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

Step3: Simplify the expression

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

Answer:

$M=\log\frac{10S}{S}$ (or $M = \log 10$) which is equivalent to the fourth option $M=\log\frac{10}{S}$ (since $\log\frac{10S}{S}=\log 10+\log\frac{S}{S}=\log 10+0=\log\frac{10}{S}$ when using the logarithm property $\log\frac{a}{b}=\log a-\log b$ and $\log\frac{S}{S} = 0$)