If sum of all roots of equation e2x−11ex−45e−x+812=0 is logep then P =

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If sum of all roots of equation $e^{2 x} - 11 e^{x} - 45 e^{- x} + \frac{81}{2} = 0$ is $\log_{e} p$ then P =

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${(e^{x})}^{3} - 11 {(e^{x})}^{2} - 45 + \frac{81}{2} e^{x} = 0$

$2 t^{3} - 22 t^{2} + 81 t - 90 = 0$

$t_{1} t_{2} t_{3} = 45$

$e^{x_{1}} e^{x_{2}} e^{x_{3}} = 45$

${\log_{e} x_{1} + x_{2} + x_{3}}^{} = \log_{e} 45$

$P = 45$

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