Question

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.
-1.5
-0.5
1.5
3.6

Explanation:

Step1: Set up the intensity relationship

Given that the intensity of the earthquake $I$ is 35 times the intensity of a standard earthquake $S$, so $I = 35S$.

Step2: Substitute into the magnitude - formula

Substitute $I = 35S$ into the formula $M=\log\frac{I}{S}$. We get $M=\log\frac{35S}{S}$.

Step3: Simplify the expression

Since $\frac{35S}{S}=35$, then $M = \log(35)$.

Step4: Calculate the value

Using a calculator, $\log(35)\approx1.544$. Rounding to the nearest tenth, $M\approx1.5$.

Answer:

C. 1.5