According to the US Geological Survey, the number of kilograms of TNT you would need to detonate to release the same amount of energy as an earthquake is given by the formula below, in which M is the earthquake magnitude.

If an earthquake released four billion kg of TNT worth of energy, what magnitude was it? Round your answer to two digits after the decimal.




The formula given by the U.S. Geological Survey to relate earthquake magnitude \( M \) to the amount of energy \( E \) in kilograms of TNT is:

\[
E = 10^{1.5M + 4.8}
\]

Where:
- \( E \) is the energy released in kilograms of TNT.
- \( M \) is the earthquake magnitude.

We are given that \( E = 4 \times 10^9 \) kg (four billion kg of TNT). To find \( M \), we need to solve the equation for \( M \).

1. Start with the formula:

\[
4 \times 10^9 = 10^{1.5M + 4.8}
\]

2. Take the logarithm (base 10) of both sides:

\[
\log(4 \times 10^9) = 1.5M + 4.8
\]

3. Solve for \( M \):

\[
M = \frac{\log(4 \times 10^9) - 4.8}{1.5}
\]

Let me calculate this.

According to the US Geological Survey, the number of kilograms of TNT you would need to detonate to release the same amount of energy as an earthquake is given by the formula below, in which M is the earthquake magnitude.

If an earthquake released four billion kg of TNT worth of energy, what magnitude was it? Round your answer to two digits after the decimal.

Learn how to calculate the magnitude of an earthquake that releases energy equivalent to four billion kilograms of TNT using the logarithmic formula provided by the US Geological Survey. The step-by-step solution includes applying logarithmic properties and solving for the earthquake magnitude. Suitable for students in Grades 10-12.

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