$\begin{array} { l }5=3\ln\left({x}\right)-\frac{ 1 }{ 2 } \times \ln\left({x}\right),& x > 0\end{array}$
Calculate the difference$5=\frac{ 5 }{ 2 } \times \ln\left({x}\right)$
Swap the sides of the equation$\frac{ 5 }{ 2 } \times \ln\left({x}\right)=5$
Multiply both sides of the equation by $\frac{ 2 }{ 5 }$$\ln\left({x}\right)=2$
Convert the logarithm into exponential form using the fact that $\ln\left({x}\right)=b$ is equal to $x={e}^{b}$$\begin{array} { l }x={e}^{2},& x > 0\end{array}$
Check if the solution is in the defined range$\begin{align*}&x={e}^{2} \\&x\approx7.38906\end{align*}$