6.6 Exercise 116

Use a calculator to solve the equation. Unless indicated otherwise, round all answers to the nearest ten-thousandth.

The magnitude M of an earthquake is represented by the equation $M = \frac{2}{3} \log \left(\frac{E}{E_{0}}\right)$ where $E$ is the amount of energy released by the earthquake in joules and $E_{0} = 10^{4.4}$ is the assigned minimal measure released by an earthquake. To the nearest hundredth, what would the magnitude be of an earthquake releasing $1.4 \cdot 10^{13}$ joules of energy?