Find limit as x approaches infinity of (1-(2/x))^3x

Let L = lim(x→∞) (1 - 2/x)^(3x).

Take natural logs of both sides:
ln L = lim(x→∞) 3x ln(1 - 2/x) = lim(x→∞) 3 ln(1 - 2/x) / (1/x).

Letting t = 1/x yields
ln L = lim(t→0+) 3 ln(1 - 2t) / t.
.......= lim(t→0+) 3 * -2/(1 - 2t) / 1, by L'Hopital's Rule
.......= -6.

Hence, L = e^(-6).

I hope this helps!