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We can compare the intensities of earthquakes using the Richter scale $M=\log\frac{I}{S}$ . On $21/11/2022$ , West Java recorded an earthquake with magnitude $M=5.6$ . This was the deadliest earthquake to hit Indonesia since the $28/9/2018$ Sulawesi earthquake. The Sulawesi earthquake had a magnitude of $M=7.5$ . How many times more intense was the first earthquake than the second earthquake?

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Find a value using two-variable equations: word problems

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Q. We can compare the intensities of earthquakes using the Richter scale

M=\log\frac{I}{S}

. On

21/11/2022

, West Java recorded an earthquake with magnitude

M=5.6

. This was the deadliest earthquake to hit Indonesia since the

28/9/2018

Sulawesi earthquake. The Sulawesi earthquake had a magnitude of

M=7.5

. How many times more intense was the first earthquake than the second earthquake?

Understand Richter scale formula: Understand the Richter scale formula. $\newline$ The Richter scale is given by $M = \log(\frac{I}{S})$ , where $M$ is the magnitude on the Richter scale, $I$ is the intensity of the earthquake, and $S$ is a standard intensity. To compare the intensities of two earthquakes, we can use the formula to find the ratio of their intensities.
Calculate intensity ratio: Calculate the intensity ratio using the magnitudes of the two earthquakes. Let $I_1$ be the intensity of the West Java earthquake and $I_2$ be the intensity of the Sulawesi earthquake. We have $M_1 = 5.6$ for the West Java earthquake and $M_2 = 7.5$ for the Sulawesi earthquake. The ratio of the intensities can be found using the formula $10^{(M_2 - M_1)} = \frac{I_2}{I_1}$ .
Substitute given magnitudes: Substitute the given magnitudes into the formula. $\newline$ $10^{(M2 - M1)} = 10^{(7.5 - 5.6)} = 10^{1.9}$
Calculate intensity ratio: Calculate the intensity ratio. $10^{1.9}$ is the ratio of the intensity of the Sulawesi earthquake to the intensity of the West Java earthquake. Using a calculator, we find that $10^{1.9}$ is approximately $79.43$ .
Interpret result: Interpret the result. $\newline$ The calculation shows that the Sulawesi earthquake was approximately $79.43$ times more intense than the West Java earthquake.

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