Given:
Intensity of earthquake is 5011 times more than
To find:
The magnitude of an earthquake that is 5011 times more than a standard earthquake.
Solution:
The magnitude of an earthquake:
[tex]$M=\log \left(\frac{I_{1}}{I_{0}}\right)[/tex]
where [tex]I_1[/tex] is the measured intensity of earthquake and
[tex]I_0[/tex] is the standard intensity of earthquake
Given 5011 times more than a standard earthquake.
[tex]I_{1}=5011 I_{0}[/tex]
Substitute this into the magnitude.
[tex]$M=\log \left(\frac{5011 I_{0}}{I_{0}}\right)[/tex]
Cancel both [tex]I_0[/tex] in the numerator and denominator.
[tex]M=\log (5011)[/tex]
[tex]M=3.6999[/tex]
M = 3.7
The magnitude of the earthquake is 3.7.
