Question

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:

Answer 1

The answer is "158.489"

Explanation:

for san francisco earthquake:

`\log((a_1)/(T)) + B = 7.8\\\\\log((a_1)/(T))+\log(10^(B)) = 7.8\\\\\log((a_1)/(T) * 10^(B))=7.8\\\\((a_1)/(T) * 10^B=10^(7.8)...............(i)`

similarly , for coloumbia earthquake:

`(a_2)/(T)* 10^B = 10^(5.6).................(ii)`

divide equation (i) and (ii):

`(a_1)/(a_2)=(10^(7.8))/(10^(5.6))\\\\(a_1)/(a_2)=10^(2.2)\approx 158.489`