1. ## simple logs

Hello there,

Im a little stuck on this:

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

it says hint use e^2x = ((e^x)^2)

im meant to get 0 but i get 0.23...
can you help?

2. Originally Posted by darksupernova
Hello there,

Im a little stuck on this:

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

it says hint use e^2x = ((e^x)^2)

im meant to get 0 but i get 0.23...
can you help?
$e^{2x} + e^x - 2 = 0$

$(e^x)^2 + e^x - 2 = 0$.

You have a quadratic equation in $e^x$. So let $X = e^x$ so that the equation looks like

$X^2 + X - 2 = 0$

$(X + 2)(X - 1) = 0$

So $X = -2$ or $X = 1$.

Therefore $e^x = -2$ or $e^x = 1$.

But since $e^x > 0$ for all $x$, that means that only the second case is possible.

So $e^x = 1$

$x = \ln{1}$

$x = 0$.

3. i didnt spot that! Thanks very much!