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

We'll apply substitution technique to solve the
exponential equation.

e^x =
t

We'll raise to square both
sides:

e^2x = t^2

t^2 - 6t + 5
= 0

We'll apply quadratic
formula:

t1 = [6+sqrt(36 -
20)]/2

t1 = (6 + 4)/2

t1 =
5

t2 = 1

But e^x = t1
=> e^x = 5

We'll take natural logarithms both
sides:

ln e^x = ln 5

x*ln e =
ln 5

x = ln 5

e^x =
t2=> e^x = 1

x =
0

The solutions of the equation are: {0 ; ln
5}.