Question

By what approximate factor is the intensity of an earthquake with magnitude 5.4 greater than an earthquake with magnitude 5.3?

Answer 1

I think you forgot to give the options along with the question. I am answering the question based on my knowledge and research. "1.26 times" would be the approximate factor by which the intensity of an earthquake with magnitude 5.4 is greater than an earthquake with magnitude 5.3. I hope the answer has helped you.

Answer 2

The equation for the magnitude of an earthquake is given by

$M=log(\frac{I}{I_{0} } )$.

Here, I is the intensity of earthquake and ${I_{0}$ is constant.

For an earthquake with magnitude 5.4,

$5.4= log(\frac{I_{1} }{I_{0} })$.

Similarly for an earthquake with magnitude 5.3,

$5.3= log(\frac{I_{2} }{I_{0} })$.

Therefore,

$\frac{log(\frac{I_{1} }{I_{0} })}{log(\frac{I_{2} }{I_{0} })} =\frac{5.4 }{5.3 } \\\\(\frac{I_{1} }{I_{2} })=\frac{10^{5.4} }{10^{5.3} }\\\\(\frac{I_{1} }{I_{2} }) =10^{5.4-5.3}=1.2589\simeq 1.3\\\\I_{1} =1.3I_{2}$

Thus, the intensity of an earthquake with magnitude 5.4 greater than an earthquake with magnitude 5.3 is about 1.3 times greater.