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

Answer:

The answer is "158.489"

Step-by-step explanation:

for san francisco earthquake:

$\log(\frac{a_1}{T}) + B = 7.8\\\\\log(\frac{a_1}{T})+\log(10^{B}) = 7.8\\\\\log(\frac{a_1}{T} \times 10^{B})=7.8\\\\(\frac{a_1}{T} \times 10^B=10^{7.8}...............(i)$

similarly , for coloumbia earthquake:

$\frac{a_2}{T}\times 10^B = 10^{5.6}.................(ii)$

divide equation (i) and (ii):

$\frac{a_1}{a_2}=\frac{10^{7.8}}{10^{5.6}}\\\\\frac{a_1}{a_2}=10^{2.2}\approx 158.489$