Measured on the Richter​ scale, the magnitude of an earthquake of intensity I is defined as Upper R equals log left parenthesis Upper I divided by Upper I 0 right parenthesis where Upper I 0 is a minimum level for comparison. What is the Richter scale reading for the earthquake for which Upper I equals 77 comma 000 comma 000 Upper I 0​?

The Richter scale reading \( R \) is defined by the formula:

\[
R = \log\left(\frac{I}{I_0}\right)
\]

where:
- \( I \) is the intensity of the earthquake,
- \( I_0 \) is the reference minimum intensity.

You are given that \( I = 77,000,000 \, I_0 \). Substituting this into the formula:

\[
R = \log\left(\frac{77,000,000 \, I_0}{I_0}\right)
\]

Since the \( I_0 \) terms cancel out, you have:

\[
R = \log(77,000,000)
\]

Now, let's calculate \( \log(77,000,000) \).

\[
\log(77,000,000) \approx 7.886
\]

Thus, the Richter scale reading for this earthquake is approximately 7.89.

Would you like more details on this solution, or do you have any other questions?

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Here are five related questions:
1. How is the Richter scale logarithmic, and what does it imply about earthquake intensity?
2. What happens if the intensity is halved? How would that affect the Richter reading?
3. What is the relationship between an increase of 1 on the Richter scale and the intensity of the earthquake?
4. Can the Richter scale have negative values, and if so, what would that mean?
5. What are some other scales used to measure earthquake intensity, and how do they compare to the Richter scale?

**Tip**: A one-unit increase on the Richter scale represents a tenfold increase in measured amplitude and roughly 31.6 times more energy release.

Measured on the Richter scale, the magnitude of an earthquake of intensity I is defined as R = log(I / I0) where I0 is a minimum level for comparison. What is the Richter scale reading for the earthquake for which I = 77,000,000 I0?

Discover how to calculate the Richter scale reading for an earthquake with an intensity of 77,000,000 times the minimum reference level. This problem involves logarithmic concepts and uses the Richter scale formula, making it ideal for high school students in Grades 9-12.

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