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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][tex]$I_0$[/tex][/tex]. The formula is given by [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 solve this problem, we need to start with the given formula for the Richter scale magnitude:
[tex]\[ M = \log \left(\frac{I}{I_0}\right) \][/tex]

Here:
- [tex]\( M \)[/tex] is the Richter scale magnitude.
- [tex]\( I \)[/tex] represents the intensity of the earthquake we need to find.
- [tex]\( I_0 \)[/tex] is the intensity of the reference earthquake.

In this problem, we are given:
- The magnitude [tex]\( M \)[/tex] is 4.8.
- The intensity of the reference earthquake [tex]\( I_0 \)[/tex] is 1.

Now, substitute the given values into the formula:
[tex]\[ 4.8 = \log \left(\frac{I}{1}\right) \][/tex]

Since dividing by 1 does not change the value of [tex]\( I \)[/tex]:
[tex]\[ 4.8 = \log (I) \][/tex]

Therefore, the equation that can be used to find the intensity [tex]\( I \)[/tex] of the earthquake is:
[tex]\[ 4.8 = \log (I) \][/tex]

This matches option C.

So, the correct answer is:
[tex]\[ \boxed{C} \][/tex]

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