Answer
The simplified value is $ R=3$.
Work Step by Step
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$.
