which equation represents the magnitude of an earthquake that is 100 times more intense than a standard…

which equation represents the magnitude of an earthquake that is 100 times more intense than a standard earthquake?\n$m = \\log\\frac{i}{100s}$\n$m = \\log\\frac{100s}{s}$\n$m = \\log(100s)$\n$m = \\log\\frac{100}{s}$\ncomplete\nthe magnitude is $m=$\ndone

which equation represents the magnitude of an earthquake that is 100 times more intense than a standard earthquake?\n$m = \\log\\frac{i}{100s}$\n$m = \\log\\frac{100s}{s}$\n$m = \\log(100s)$\n$m = \\log\\frac{100}{s}$\ncomplete\nthe magnitude is $m=$\ndone

Answer

Answer:

  1. $M = \log\frac{100S}{S}$; 2. $2$

Explanation:

Step1: Recall magnitude formula

The magnitude formula for an earthquake is $M=\log\frac{I}{S}$, where $I$ is the intensity of the earthquake and $S$ is the intensity of a standard - earthquake. Given that $I = 100S$ (since the earthquake is 100 times more intense than a standard earthquake). Substitute $I = 100S$ into the formula: $M=\log\frac{100S}{S}$.

Step2: Simplify the expression

$\frac{100S}{S}=100$, so $M=\log(100)$. Since $100 = 10^{2}$ and $\log_{10}(10^{x})=x$, then $\log(100)=\log(10^{2}) = 2$.