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 35 times more intense than a standard earthquake? use a calculator. round your answer to the nearest tenth.\n-1.5\n-0.5\n1.5\n3.6
Answer
Explanation:
Step1: Identify the intensity relationship
Given that the earthquake is 35 times more intense than a standard earthquake, so $I = 35S$.
Step2: Substitute into the magnitude formula
Substitute $I = 35S$ into $M=\log\frac{I}{S}$, we get $M=\log\frac{35S}{S}$.
Step3: Simplify the expression
$\frac{35S}{S}=35$, so $M = \log(35)$.
Step4: Calculate the value
Using a calculator, $\log(35)\approx1.544$. Rounding to the nearest tenth gives $M\approx1.5$.
Answer:
C. 1.5