Step 1
Given;
[tex]\begin{gathered} First\text{ earthquake\lparen M}_a)\text{ =7.9} \\ second\text{ earthquake\lparen M}_b)\text{=4.1} \end{gathered}[/tex]
Step 2
State the magnitude and intensity formula we can use to solve this problem
[tex]\begin{gathered} M_a=log(\frac{I_a}{I_o}_)) \\ M_b=log(\frac{I_b}{I_o}) \end{gathered}[/tex][tex]\begin{gathered} 10^{7.9}=\frac{I_a}{I_o} \\ 10^{4.1}=\frac{I_b}{I_o} \\ \end{gathered}[/tex][tex]Solve\text{ for I}_a\text{ and I}_b[/tex][tex]\begin{gathered} 10^{7.9}(I_o)=I_a \\ 10^{4.1}(I_o)=I_b \\ \frac{I_a}{I_b}=\frac{10^{7.9}(I_o)}{10^{4.1}(I_o)}=10^{7.9-4.1}=10^{3.8} \\ =6309.573445 \\ \approx6310\text{ times as intense} \end{gathered}[/tex]
Answer;
[tex]6310\text{ times as intense}[/tex]
