Question

The energy E (in ergs) released by an earthquake is approximated by log E= 11.8 + 1.5M. Where M is the magnitude of the earthquake. What is the energy released by the 1906 San Francisco quake, which measured 8.3 on the Richter scale? This energy, it is estimated, would be sufficient to provide the entire world's food requirements for a day. Answer in ergs.

Answer 1

`\large \boxed{3.4 * 10^(10)\text{ ergs }}`

Explanation:

`\begin{array}{rcl}\log E & = & 11.8 + 1.5M\\& = & 11.8 + 1.5 * 8.3\\& = & 11.8 + 12.45\\& = & 24.25\\E & = & e^(24.25)\\& = & \mathbf{3.4 * 10^(10)} \textbf{ ergs}\\\end{array}\\\text{ The energy released was $\large \boxed{\mathbf{3.4 * 10^(10)}\textbf{ ergs }}$}`