Solve for x the equation e^2x-6*e^x+5=0

The equation e^2x-6*e^x+5=0 has to be
solved.

e^2x-6*e^x+5=0

=
(e^x)^2-6*e^x+5=0

= (e^x)^2-5*e^x - e^x
+5=0

= e^x*(e^x - 5) - 1(e^x -
5)=0

= (e^x - 1)*(e^x -
5)=0

e^x - 1 = 0

e^x =
1

This is the case when x =
0

e^x - 5 = 0

e^x =
5

Take the natural logarithm of both the
sides

x = ln 5

The solution of
the equation e^2x-6*e^x+5=0 is x = 0 and x = ln 5