Question

E^(2x) — 3e^x + 2 = 0
Solve for x

Answer 1

To solve the equation e^(2x) — 3e^x + 2 = 0 for x, substitute y = e^x, factorize the quadratic equation, and solve for x.

Step-by-step explanation:

To solve the equation e^(2x) — 3e^x + 2 = 0 for x,

1. Let's make a substitution. Let y = e^x.
2. Then the equation becomes y^2 - 3y + 2 = 0.
3. Now we can factorize it as (y - 1)(y - 2) = 0.
4. So the two possible values of x are x = ln(1) and x = ln(2).
5. Since ln(1) equals 0, our final solution is x = ln(2).

Answer 2

You can essentially treat this equation as a factorable quadratic, with the variable being
`e^x`:


`e^(2x) - 3e^x + 2 = 0`

`(e^x - 2)(e^x - 1) = 0`

`e^x = 1, 2`

`x = \ln 1, \ln 2 = 0, \ln 2`