# Math Help - Solve e^(2x) - e^x - 6 = 0 for x. Can't seem to set this up correctly!

1. ## Solve e^(2x) - e^x - 6 = 0 for x. Can't seem to set this up correctly!

I need help setting up this properly... Solve e^(2x) - e^x - 6 = 0 for x.

2. Originally Posted by ktehspynx
I need help setting up this properly... I keep running into dead ends! Do I need to make some sort of substitution? Please help, I'd really appreciate it!
$e^{2x} - e^x - 6 = 0$

$e^{x} e^x - e^x - 6 = 0$

This looks like a quadratic equation to me

Let $e^x = u$

$u^2 - u - 6 = 0$

$(u-3)(u+2) = 0$

It follows that,

$e^x = 3$ and $e^x = -2$

But since the negative root produces imaginary values, we will leave it

Take,

$e^x = 3$

$x = ln3$

3. Ah, I see it now! Thanks so much.