## Precalculus (6th Edition) Blitzer

The simplified value is $R=3$.
We know that the intensity of the earthquake is represented by $1000{{I}_{o}}$. So, $I=1000{{I}_{o}}$ Put the value of I in $R=\log \left( \frac{I}{{{I}_{o}}} \right)$, \begin{align} & R=\log \left( \frac{1000{{I}_{o}}}{{{I}_{o}}} \right) \\ & =\log \left( 1000 \right) \end{align} As ${{10}^{3}}=1000$ Rewrite the above exponential form with logarithms: If ${{b}^{y}}=x$, then ${{\log }_{b}}x=y$, Then, ${{10}^{3}}=1000$ is equivalent to $\log \left( 1000 \right)=3$. Thus, the magnitude on the Richter scale is $R=3$.