Solve the equation e^(2x) - 5e^x + 6 = 0
To solve the equation e^(2x) - 5e^x + 6 = 0, we can make a substitution. Let y = e^x. Then, our equation becomes:

y^2 - 5y + 6 = 0

This is a quadratic equation, which we can factor as (y-3)(y-2) = 0. This gives us two possible solutions for y:

1. y = 3
2. y = 2

Now, recall that we let y = e^x. So, we have two equations to solve for x:

1. e^x = 3
2. e^x = 2

To solve these equations, we take the natural logarithm of both sides:

1. ln(e^x) = ln(3)
   x = ln(3)

2. ln(e^x) = ln(2)
   x = ln(2)

So, there are two solutions for x: x = ln(2) and x = ln(3).