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. what is the magnitude of an earthquake that is 1,000 times more intense than a standard earthquake? use a calculator. round your answer to the nearest tenth.\no 2\no 3\no 4.5\no 6.9

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. what is the magnitude of an earthquake that is 1,000 times more intense than a standard earthquake? use a calculator. round your answer to the nearest tenth.\no 2\no 3\no 4.5\no 6.9

Answer

Explanation:

Step1: Set up the intensity relationship

Given that the intensity of the earthquake $I$ is 1000 times the intensity of a standard earthquake $S$, so $I = 1000S$.

Step2: Substitute into the magnitude formula

Substitute $I = 1000S$ into $M=\log\frac{I}{S}$, we get $M=\log\frac{1000S}{S}$.

Step3: Simplify the expression

$\frac{1000S}{S}=1000$, so $M = \log(1000)$. Since $1000 = 10^3$, and $\log_{10}(10^x)=x$, then $M=\log(10^3)=3$.

Answer:

B. 3