Limits as n goes to infinity

1. TranscendArcu

288
1. The problem statement, all variables and given/known data

3. The attempt at a solution
So I know that the limit as $n → ∞$ of $(1 - \frac{1}{n})^n = \frac{1}{e}$. Using this information, is it legitimate to observe:

The limit as $n → ∞$ of $(1 - \frac{1}{n})^{n ln(2)} =$ the limit as $n → ∞$ of $((1 - \frac{1}{n})^n)^{ln(2)} = e^{-1 ln(2)} = e^{ln(\frac{1}{2})} = \frac{1}{2}$

2. Robert1986

828
Looks good to me.

3. Dick

25,887
Looks ok to me.