Answer:
Option D. 2.51 is correct.
Step-by-step explanation:
Magnitude of first earthquake = 8.6
Let intensity of first earthquake be x
\(Magnitude = \log(\frac{x}{S}),\text{ where S is seismographic factor}\\\\\implies 8.6=\log(\frac{x}{S}).......(1)\)
Magnitude of second earthquake = 8.2
Let intensity of second earthquake be y
\(Magnitude = \log(\frac{y}{S}),\text{ where S is seismographic factor}\\\\\implies 8.2=\log(\frac{y}{S}).......(2)\)
Now, to find the factor by which intensity of first earthquake is greater than intensity of second : we divide equation (1) by equation (2)
\(\implies\log(\frac{x}{y})=8.6 - 8.2\\\\\implies \log(\frac{x}{y})=0.4\\\\\implies\frac{x}{y}=10^{0.4}\\\\\implies\frac{x}{y}=2.51\)
Hence the required factor is 2.51
Therefore, Option D. 2.51 is correct.
