Question

lim as x->ln2 of ((e^3x)-8)/((e^2x)-4)

Answer 1

\[\lim_{x \rightarrow \ln2}(e ^{3x}-8)/(e ^{2x}-4)\]

\[e ^{lnx}=x\] and \[3\ln x = (\ln x)^3\] that should help you get to the answer. Let me know if you need more help

Answer 2

And make use of De L'Hôpital.

Answer 3

I would use the substitution,
$$y=e^x$$
then,
$$x\to \ln 2 \implies y\to 2$$
$$\begin{align*}
\lim\limits_{x\to \ln2} \frac{e^{3x}-8}{e^{2x}-4}&=\lim\limits_{y\to2}\frac{y^3-8}{y^2-4}
\end{align*}$$

Answer 4

Thanks everyone! Azolator, I almost got it with your hints but BAdhi's method of substitution was so slick.

Answer 5

I just want to point out that BAdhi's substitution worked because of those properties so make sure you know why you can substitute some things and not others