Answer:
6.31 times ( approx )
Explanation:
Given formula to find the magnitude of an earthquake is,
[tex]M=log(\frac{I}{S})[/tex]
Where,
I = intensity of the earthquake being measured,
S = the intensity of a standard earthquake,
By the above formula,
[tex]10^{M}=\frac{I}{S}[/tex]
[tex]\implies I = S\times 10^{M}[/tex]
Since, S is constant,
If M = 7.5,
Then intensity of the earthquake,
[tex]I_1=S\times 10^{7.5}[/tex]
If M = 6.7,
Then intensity of the earthquake,
[tex]I_2=S\times 10^{6.7}[/tex]
[tex]\frac{I_1}{I_2}=\frac{S\times 10^{7.5}}{S\times 10^{6.7}}=10^{7.5-6.7}=10^{0.8}\approx 6.31[/tex]
[tex]\implies I_1=6.31I_2[/tex]
Hence, the earthquake that measures 7.5 on the Richter scale is 6.3 times more intense than the earthquake that measures 6.7.
