Find the best solutions to your questions at Westonci.ca, the premier Q&A platform with a community of knowledgeable experts. Join our Q&A platform to connect with experts dedicated to providing precise answers to your questions in different areas. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

Select the correct answer.

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]


Sagot :

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]