Question

select the correct answer.
the richter scale measures the magnitude, m, of an earthquake as a function of its intensity, i, and the intensity of a reference earthquake (m = log(\frac{i}{i_0}))
which equation calculates the magnitude of an earthquake with an intensity 10,000 times that of the reference earthquake?
a. (m=log(10,000))
b. (m = log(\frac{1}{10,000}))
c. (m=log(\frac{i}{10,000}))
d. (m=log(\frac{10,000}{i_0}))

Explanation:

Step1: Identify given relationship

The formula for magnitude is $M = \log(\frac{I}{I_0})$.

Step2: Substitute intensity value

Given that $I = 10000I_0$. Substitute $I$ in the formula: $M=\log(\frac{10000I_0}{I_0})$.

Step3: Simplify the fraction

$\frac{10000I_0}{I_0}=10000$, so $M = \log(10000)$.

Answer:

A. $M=\log(10,000)$