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 astandard 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.
o 2
o 3
o 4.5
o 6.0

Explanation:

Step1: Set up the intensity relationship

Given that $I = 1000S$.

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 fraction

$\frac{1000S}{S}=1000$, so $M = \log(1000)$.

Step4: Evaluate the logarithm

Since $10^3=1000$, $\log(1000)=3$.

Answer:

B. 3