In 1935 Charles Richter and Beno Gtenberg of (mathrm{Cal}) Tech used a new scale for measuring earthquakes

In 1935 Charles Richter and Beno Gütenberg of \(\mathrm{Cal}\) Tech used a new scale for measuring earthquakes in California. This scale is now universally used to measure the strength of earthquakes. It relates the energy \(E\) (in ergs) to the magnitude of the earthquake \(M\) by the formula

\[M=\frac{\log E-11.8}{1.5}\]

a. A small earthquake is one that releases \(15^{15}\) ergs of energy. What is the magnitude (to the nearest hundredth) of such an earthquake on the Richter scale?

b. A large earthquake is one that releases \(10^{25}\) ergs of energy. What is the magnitude (to the nearest hundredth) of such an earthquake on the Richter scale?

c. How much energy is released in an 8.0 earthquake?

d. Solve for \(E\).