Question

3.
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
Columbia earthquake below (view image)


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

Using the properties of logarithms, it is found that the San Francisco earthquake was 24.71 times more severe 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 $R_1, R_2, R_1 > R_2$, the ratio of the intensities is given by:

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

For this problem, the intensities are:

$R_1 = 7.8, R_2 = 5.6$

Hence the ratio is:

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

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

More can be learned about logarithms at https://brainly.com/question/20719486

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