If the sum of all the roots of the equation

${e^{2x}} - 11{e^x} - 45{e^{ - x}} + {{81} \over 2} = 0$ is ${\log _e}p$, then p is equal to ____________.

Given that <br/><br/>$e^{2 x}-11 e^x-45 e^{-x}+\frac{81}{2}=0$ <br/><br/>$\Rightarrow 2 e^{3 x}-22 e^{2 x}-90+81 e^x=0$ <br/><br/>$\Rightarrow 2\left(e^x\right)^3-22\left(e^x\right)^2+81 e^x-90=0$ <br/><br/>Let $ e^x=y$ <br/><br/>$\Rightarrow 2 y^3-22 y^2+81 y-90=0$ <br/><br/>Product of roots $\left(y_1, y_2, y_3\right)$ <br/><br/>$y_1 \cdot y_2 \cdot y_3=\frac{-(-90)}{2}=45$ <br/><br/>Let $x_1, x_2$, and $x_3$ be roots of given equation <br/><br/>$\Rightarrow e^{x_1} \cdot e^{x_2} \cdot e^{x_3} = 45$ <br/><br/>$\Rightarrow e^{x_1+x_2+x_3} =45$ <br/><br/>$\Rightarrow x_1+x_2+x_3 =\log _e 45=\log _e p$ <br/><br/>$\Rightarrow p = 45$