Question #268100

The magnitude of an earthquake is given by 𝑀 = log 𝐼


where M is the Richter scale value of an earthquake, and I is the intensity of the earthquake. An earthquake of magnitude 6.4 is measured and the following aftershock has a magnitude or 4.1.


Determine algebraically how many times more intense, to the nearest whole, the earthquake is compared to the aftershock.


1
Expert's answer
2021-11-22T13:52:22-0500
M=log10I=>I=10MM=\log_{10}I=>I=10^M

IEIafter=10ME10Mafter=10MEMafter\dfrac{I_E}{I_{after}}=\dfrac{10^{M_E}}{10^{M_{after}}}=10^{M_E-M_{after}}

=106.44.1=102.3200=10^{6.4-4.1}=10^{2.3}\approx200

An earthquake is 200 times more intense in comparison with the following aftershock.


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