Please explain the answer and the steps you took to get to it. Thanks! The equat

Question

Please explain the answer and the steps you took to get to it. Thanks!

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? (A) I_1995 = 100/2004 Correct Answer (B) I_1995 = 2I_2004 (C) I_1995 = I_2004 + 2 (D) I_1995 = I_2004 +100 (E) I_1995 = 2I_2004 + 100

Explanation / Answer

let the intensity of 1995 earthquake = X

and intensity of 2004 earthquake = Y

magnitude of earthquake in 1995 = 9

9 = log ( I / K )

9 = log ( X / K )

9 = log X - log K

log X = 9 + log K

similarly

7 = log ( Y /K )

log Y = 7 + log K

subtracting the 2 equations

log X = 9 + log K

- log Y = 7 + log K

-----------------------------

log X - log Y = 2

log X = 2 + log Y

now writing 2 in the form of log

2 = log 100

so we can write

log X = log 100 + log Y

log X = log ( 100 Y )

so we can conclude

X = 100 Y

hence , intensity of 1995 = 100 * intensity of 2004

option A is correct

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