(16e^x) - (16e^2x) = 3
and the answer says that x = 0.25 but i can't see how you can get there? please help, much appreciated!! thanks!
Rewrite it as $\displaystyle \displaystyle 0 = 16e^{2x} - 16e^x + 3$
$\displaystyle \displaystyle 0 = 16\left(e^x\right)^2 - 16e^x + 3$.
Now let $\displaystyle \displaystyle X = e^x$ so that the equation becomes
$\displaystyle \displaystyle 0 = 16X^2 - 16X + 3$, which is a quadratic equation you can solve for $\displaystyle \displaystyle X$, and then solve for $\displaystyle \displaystyle x$.