Question

On the Richter scale, earthquake A is estimated to be 3.0 and Earthquake B is estimated to be 1.5. How much stronger is earthquake A?

Answer 1

In order to calculate the difference of the two earthquakes, we use the formula below:

`M_A-M_B=log\text{ }x`

where x is the difference in the intensity of the earthquakes in terms of Earthquake A and M are the magnitudes of each earthquake.

Ma = 3.0, Mb = 1.5

Let's plug these values into the formula above and solve.

`3.0-1.5=log\text{ }x`

a. Subtract the two magnitudes. The new equation will be:

`1.5=log\text{ }x`

b. Convert the logarithmic function into an exponential function.

`10^(1.5)=x`

c. Apply the exponent to its base 10.

`\begin{gathered} 31.6227=x \\ 32\approx x \end{gathered}`

Therefore, Earthquake A is 32 times stronger than Earthquake B.