# Evaluate: 1 (8)/(9) * (6)/(11)

## Expression: $5=3\ln\left({x}\right)-\frac{ 1 }{ 2 } \times \ln\left({x}\right)$

Determine the defined range

$\begin{array} { l }5=3\ln\left({x}\right)-\frac{ 1 }{ 2 } \times \ln\left({x}\right),& x > 0\end{array}$

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*}

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