Answer
The solution of the giving expression is $ x=9$.
Work Step by Step
It is given that ${{\log }_{2}}\left( \frac{x+9}{x} \right)=1$
$\begin{align}
& \log \left( \frac{x+9}{x} \right)=\log \,2 \\
& \frac{x+9}{x}=2 \\
& x+9=2x \\
& x=9
\end{align}$
Therefore, the solution of the giving expression is $ x=9$.
