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
Answer
Answer:
B. 3
Explanation:
Step1: Set up the intensity relationship
Given that $I = 1000S$.
Step2: Substitute into magnitude formula
$M=\log\frac{I}{S}=\log\frac{1000S}{S}$.
Step3: Simplify the fraction
$\frac{1000S}{S}=1000$, so $M = \log(1000)$.
Step4: Evaluate the logarithm
Since $10^3=1000$, $\log(1000)=3$.