Solving a 5.4 Earthquake Aftershock: Round to 1 Decimal Place

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To find the magnitude of the aftershock following a 5.4 magnitude earthquake, first calculate the intensity (I) of the original quake using the formula M=log(I/I0). The intensity of the aftershock is then determined by dividing the original intensity by 39. Finally, the magnitude of the aftershock can be computed using the difference in magnitudes formula, M1 - M2 = log(I1/I2). After performing these calculations, the aftershock's magnitude should be rounded to one decimal place. This method accurately determines the aftershock's magnitude based on the given intensity relationship.
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Can someone please solve this . I have been trying to solve this from last 2 days.
1. Question
  1. An earthquake with a magnitude of 5.4 is 39 times as intense as an aftershock that occurs five hours later. What is the magnitude of the aftershock? Round your answer to one decimal place.
2. Formula Given in Text Book.
M=log(I/I0)

  • M is the magnitude
    [*]I is the intensity of the earthquake
    [*]I0 is the intensity of an earthquake with a magnitude of 0

formula for richter scale.PNG


Thanks
 

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Use the magnitude to compute the I of the original quake.

Divide that I by 39 to find the intensity of the aftershock.

Compute the mahnitude of the aftershock.
 
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If the intensity are ##I_1,~I_2,## then their magnitudes' difference can be done with ##M_1-M_2=\ln\frac{I_1}{I_0}-\ln\frac{I_2}{I_0}## right? With the information you got, try to have some attempts on it .
 
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