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?
$\displaystyle e^{2x} + e^x - 2 = 0$
$\displaystyle (e^x)^2 + e^x - 2 = 0$.
You have a quadratic equation in $\displaystyle e^x$. So let $\displaystyle X = e^x$ so that the equation looks like
$\displaystyle X^2 + X - 2 = 0$
$\displaystyle (X + 2)(X - 1) = 0$
So $\displaystyle X = -2$ or $\displaystyle X = 1$.
Therefore $\displaystyle e^x = -2$ or $\displaystyle e^x = 1$.
But since $\displaystyle e^x > 0$ for all $\displaystyle x$, that means that only the second case is possible.
So $\displaystyle e^x = 1$
$\displaystyle x = \ln{1}$
$\displaystyle x = 0$.