Answer:
2.5 times more intense.
Step-by-step explanation:
For the 6.2 magnitude earthquake, the Richter model gives us
[tex]$6.2 = log(\frac{I}{I_0} )$[/tex]
where [tex]I[/tex] is the intensity of the 6.2 earthquake.
And for the 5.8 magnitude earthquake,
[tex]$5.8 = log(\frac{I_1}{I_0} )$[/tex]
where [tex]I_1[/tex] is the intensity of the 5.8 earthquake.
Now, we subtract the two equations to get:
[tex]$6.2 -5.8 = log(\frac{I}{I_0} ) - log (\frac{I_1}{I_0} )$[/tex]
[tex]$0.4 = log(\frac{I}{I_0} ) - log (\frac{I_1}{I_0} )$[/tex]
Now using the logarithmic property
[tex]$log (a)-log(b)= log(\frac{a}{b} )$[/tex]
our equation becomes
[tex]$0.4 = log(\frac{I}{I_0} \div \frac{I_1}{I_0} )$[/tex]
[tex]$0.4 = log(\frac{I}{I_0} * \frac{I_0}{I_1} )$[/tex]
[tex]$0.4 = log(\frac{I}{I_1} )$[/tex]
take both sides to the 10th power and get:
[tex]$10^{0.4} =\frac{I}{I_1} $[/tex]
[tex]$\boxed{\frac{I}{I_1} = 2.5} $[/tex]
Therefore, the earthquake was 2.5 times more intense.
