The product of all solutions of the equation e^ 5( _ e x)^2+3 =x^8,...

The product of all solutions of the equation

\mathrm{e}^{5\left(\log _{\mathrm{e}} x\right)^2+3}=x^8, x\gt0

, is :

Options

A. $e^{8 / 5}$

\begin{aligned} & \mathrm{e}^{5(\ln x)^2+3}=\mathrm{x}^8 \\ & \Rightarrow \ell \mathrm{ne}^{5(\ln x)^2+3}=\ell \mathrm{nn}^8 \\ & \Rightarrow 5(\ln \mathrm{x})^2+3=8 \ell \mathrm{nx} \\ & (\ell \mathrm{nx}=\mathrm{t}) \\ & \Rightarrow 5 \mathrm{t}^2-8 \mathrm{t}+3=0 \\ & \quad \mathrm{t}_1+\mathrm{t}_2=\frac{8}{5} \\ & \quad \ln \mathrm{x}_1 \mathrm{x}_2=\frac{8}{5} \\ & \mathrm{x}_1 \mathrm{X}_2=\mathrm{e}^{8 / 5}\end{aligned}