Question

There was an earthquake in San Francisco April 18, 1906. More recently there was another earthquake in Columbia June 27, 2014. Earthquakes are measured using the associated amplitude on the Richter scale. Let a1 be the amplitude for the San Francisco earthquake and a2 be the amplitude for the Columbian earthquake.

San Francisco earthquake equations is below:

R1=log(a1/T)+B=7.8


Columbia earthquake equations is below:

R2=log(a2/T)+B=5.6



a. Use the properties of logs to determine how many more times severe was the San Francisco earthquake? The severity is equal to the ratio below: a1/a2

Answer 1

Solving a logarithmic equation, it is found that the San Francisco earthquake was 24.71 times more intense than the Columbian earthquake.

How to find the ratios of the intensity of earthquakes?

As given in the problem, the intensities of the earthquakes are given by logarithms of base 10. Then, supposing that the intensities are R1 and R2, with R1 greater than R2, the ratio of the intensities, that is, how much intense R1 is than R2, is given as follows:

$r = 10^{\frac{R_1}{R_2}}$

For this problem, the intensities are given as follows:

• San Francisco: R1 = 7.8.

• Columbia: R2 = 5.6.

Then, the ratio of the intensities is given as follows:

$r = 10^{\frac{7.8}{5.6}} = 24.71$

The San Francisco earthquake was 24.71 times more intense than the Columbian earthquake.

More can be learned about logarithmic equations at brainly.com/question/20719486

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