Chapter 12 - Exponential Functions and Logarithmic Functions - 12.7 Applications of Exponential Functions and Logarithmic Functions - 12.7 Exercise Set - Page 834: 22

6.

The amplitude of the earthquake is 1 million times ${{A}_{0}}$. Thus, $A=1,000,000{{A}_{0}}$. Substitute it in the formula $m=\log \frac{A}{{{A}_{0}}}$and solve as follows: $\begin{align} & m=\log \frac{A}{{{A}_{0}}} \\ & =\log \frac{1,000,000{{A}_{0}}}{{{A}_{0}}} \\ & =\log 1,000,000 \end{align}$ Therefore, $\begin{align} & m=\log 1,000,000 \\ & =6 \end{align}$