Question

The equation for the magnitude M of an earthquake is M = log (I/K) where I is the intensity of the earthquake and K is a constant. The magnitude of a 1995 earthquake was 9.0 and the magnitude of a 2004 earthquake was 7.0. Which of the following compares (I)1995, the intensity of the 1995 earthquake with (I) 2004, the intensity of the 2004 earthquake?

Multiple choice answers.
A. (I)1995= 100(I) 2004
B. (I)1995 = 2(I)2004
C. (I)1995 = (I)2004 + 2
D. (I) 1995 = (I)2004 + 100
E. (I)1995 = 2(I)2004 + 100

Answer 1

I think its C.

M = log (i/k)
M = log i - log k
a. 9 = 1995i - log k b. 7= 2004i - log k
So a-b to compare difference

therefore, 9-7 = 1995i - log k - (2004i - log k)
2 = 1995i - log k - 2004i +log k
" log k gets cancelled"
so, 2 = 1995i - 2004i
Ans.. 2 + 2004i = 1995i

Answer 2

We are given
M(I)=log(I/K)=log(I)-log(K) where K is a constant.
We also know that
\(M_{1995}=9=log(I_{1995})-log(K)\), and
\(M_{2004}=7=log(I_{2004})-log(K)\)
Subtract the two gives
\(M_{1995}-M_{2004}=9-7=2=log(I_{1995})-log(I_{2004})=log((I_{1995}/I_{2004})\)
or
\(log((I_{1995}/I_{2004})=2\)
Assuming given equation uses log to base 10, raise to power 10 on both sides give
\(I_{1995}/I_{2004}=10^2\)
and the result follows.