Question 6: The formula to measure the magnitude of earthquake is given by \(M=log_{10}\left(\frac{A}{Ao}\right)\). If amplitude \(A\) is \(10,000\) and reference amplitude \(A_o\) is \(10\). What is the magnitude of the earthquake?
Solution:
\[
\begin{align*}
M&=\log_{10}\left(\frac{A}{A_{o}}\right)\\
&=\log_{10} A-\log_{10} A_{o}\\
&=\log_{10} 10000-\log_{10} 10\\
&=4-1\\
M&=3\\
\end{align*}
\]