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Sagot :
To solve the problem of calculating the magnitude [tex]\( M \)[/tex] of an earthquake with an intensity 10,000 times that of the reference earthquake using the given intensity factor and reference intensity, we need to use the following formula:
[tex]\[ M = \log \left( \frac{I}{I_0} \right) \][/tex]
where:
- [tex]\( I \)[/tex] is the intensity of the earthquake (10,000 times the reference intensity).
- [tex]\( I_0 \)[/tex] is the reference intensity.
Given the values:
- [tex]\( I = 10,000 \)[/tex]
- [tex]\( I_0 = 4 \)[/tex]
We substitute these into the formula:
[tex]\[ M = \log \left( \frac{10,000}{4} \right) \][/tex]
This matches option D.
Therefore, the correct equation to calculate the magnitude of the earthquake is:
[tex]\[ M = \log \left( \frac{10,000}{4} \right) \][/tex]
So the correct choice is:
D. [tex]\( M = \log \left( \frac{10,000}{4} \right) \)[/tex]
[tex]\[ M = \log \left( \frac{I}{I_0} \right) \][/tex]
where:
- [tex]\( I \)[/tex] is the intensity of the earthquake (10,000 times the reference intensity).
- [tex]\( I_0 \)[/tex] is the reference intensity.
Given the values:
- [tex]\( I = 10,000 \)[/tex]
- [tex]\( I_0 = 4 \)[/tex]
We substitute these into the formula:
[tex]\[ M = \log \left( \frac{10,000}{4} \right) \][/tex]
This matches option D.
Therefore, the correct equation to calculate the magnitude of the earthquake is:
[tex]\[ M = \log \left( \frac{10,000}{4} \right) \][/tex]
So the correct choice is:
D. [tex]\( M = \log \left( \frac{10,000}{4} \right) \)[/tex]
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