Question

The magnitude M of an earthquake is given by the equation M=logE-11.81.5 , where E is the amount of energy released by the earthquake in ergs. The largest earthquake recorded in California was magnitude 11.3. How much energy was released by this earthquake?

Answer 1

Firstly, we need to replace M in the equation with the given magnitude to get the energy E released by the earthquake. In our case, the earthquake's magnitude is 11.3, thus, the equation becomes:

11.3 = (log(E) - 11.8) / 1.5

The next step is to clear the fractions by multiplying the whole equation by 1.5. Therefore, the equation becomes:

11.3 * 1.5 = log(E) - 11.8

Proceed by adding 11.8 on both sides to isolate log(E) on the right side of the equation. That brings the equation to:

11.3 * 1.5 + 11.8 = log(E)

Now, we'll have to deal with the logarithmic property of the equation. To get the value of E, we'll have to take the antilogarithm on both sides:

E = 10 ^ (11.3 * 1.5 + 11.8)

Calculating this gives us the energy released by the earthquake. It approximates to 5.623413251903537e+28 ergs. This means the earthquake released an energy of about 5.623 * 10 ^ 28 ergs.