$$ ln(({e}^{4x}*({e}^{5x})^{\frac{1}{2}})^{\frac{1}{2}}) $$
$$ \frac{1}{2}*ln(({e}^{4x}*({e}^{5x})^{\frac{1}{2}})) $$$$ \frac{1}{2}*ln(({e}^{4x}*({e}^{\frac{5x}{2}})) $$$$ \frac{1}{2}*ln({e}^{\frac{13x}{2}}) $$$$ \frac{1}{2}*\frac{13x}{2}=\frac{13x}{4}$$