Answer
$ x= \ln 1, \ln 5 $ or, $ x= 0 ; x=1.609438$
Work Step by Step
We are given that $ e^{2x}-6e^x +5=0$
or, $(e^x -5)(e^x-1) =0$
Solve by equating both factors to $0$:
$ e^5 -5 =0 \implies x =\ln 5$
and $ e^x -1 =0 \implies x= \ln 1$
So, $ x= \ln 1, \ln 5 $
or, $ x= 0 ; x=1.609438$
