Answered

Rewrite the following text for better readability, correct any grammar or spelling errors, remove unnecessary phrases, and retain the LaTeX formatting:
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[tex]$
M=\log \left(\frac{1}{4}\right)
$[/tex]

Which equation calculates the magnitude of an earthquake with an intensity 10,000 times that of the reference earthquake?

A. [tex]$M=\log (20,000)$[/tex]

B. [tex]$M=\log \left(\frac{1}{10 \pi}\right)$[/tex]

C. [tex]$M=\log \left(\text{reference}\right)$[/tex]

D. [tex]$M=\log \left(\frac{10,000}{4}\right)$[/tex]
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Response:

Which equation calculates the magnitude of an earthquake with an intensity 10,000 times that of the reference earthquake?

A. [tex]$M = \log (20,000)$[/tex]

B. [tex]$M = \log \left(\frac{1}{10 \pi}\right)$[/tex]

C. [tex]$M = \log (\text{reference})$[/tex]

D. [tex]$M = \log \left(\frac{10,000}{4}\right)$[/tex]



Answer :

GinnyAnswer
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]