e^2x-3e^x +2 =0

Let us assume that e^x =y.

Now substitute:

==> y^2 -3y +2 =0

Factorize:\

(y-2)(y-1)=0

y1= 2 ==> y1=e^x1= 2 ==> x1=ln2

y2=1 ==> y2=e^x2= 1 ==> x2=0

The solution for the equation is :

x= {0, ln2}

e^2x-3e^x +2 =0

Let us assume that e^x =y.

Now substitute:

==> y^2 -3y +2 =0

Factorize:\

(y-2)(y-1)=0

y1= 2 ==> y1=e^x1= 2 ==> x1=ln2

y2=1 ==> y2=e^x2= 1 ==> x2=0

The solution for the equation is :

x= {0, ln2}