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The Richter scale measures the magnitude, [tex]M[/tex], of an earthquake as a function of its intensity, [tex]I[/tex], and the intensity of a reference earthquake, [tex]I_0[/tex].

[tex]\[ M=\log \left(\frac{I}{I_0}\right) \][/tex]

Which equation could be used to find the intensity of an earthquake with a Richter scale magnitude of 4.8 in reference to an earthquake with an intensity of 1?

A. [tex]I=\log \left(\frac{1}{4.8}\right)[/tex]
B. [tex]4.8=\log \left(\frac{1}{I}\right)[/tex]
C. [tex]4.8=\log (I)[/tex]
D. [tex]I=\log (4.8)[/tex]



Answer :

GinnyAnswer
To determine the correct equation to find the intensity [tex]\( I \)[/tex] of an earthquake with a Richter scale magnitude of 4.8 in reference to an earthquake with an intensity of 1, we start with the given formula:

[tex]\[ M = \log \left(\frac{I}{I_0}\right) \][/tex]

Given:
- [tex]\( M = 4.8 \)[/tex]
- [tex]\( I_0 = 1 \)[/tex]

We substitute these values into the formula:

[tex]\[ 4.8 = \log \left(\frac{I}{1}\right) \][/tex]

Simplifying the fraction inside the logarithm:

[tex]\[ 4.8 = \log (I) \][/tex]

This is the equation that represents the relationship we're looking for.

Therefore, the correct equation to find the intensity [tex]\( I \)[/tex] of the earthquake is:

C. [tex]\( 4.8 = \log (I) \)[/tex]