Answer
$42.4\text{ million}$
Work Step by Step
That the magnitude $M$ of the network is $M=7.5$.
Substitute it in the formula $M=\log \frac{v}{1.34}$and solve for $v$ as follows:
$\begin{align}
& 7.5=\log \frac{v}{1.34} \\
& 7.5={{\log }_{10}}\frac{v}{1.34} \\
\end{align}$
Now convert it into an exponential equation by using the formula ${{\log }_{a}}x=m\rightarrow{{a}^{m}}=x$:
$\begin{align}
& 7.5={{\log }_{10}}\frac{v}{1.34} \\
& {{10}^{7.5}}=\frac{v}{1.34} \\
& v={{10}^{7.5}}\times 1.34
\end{align}$
Therefore,
$\begin{align}
& v={{10}^{7.57}}\times 1.34 \\
& =31622776.602\times 1.34 \\
& \approx 42,400,000 \\
& \approx 42.4\text{ million}
\end{align}$
