You can't [correction tx to @jimh, see other answer] can use L'Hopital here, [but you do not need it].
This is based upon Bernoulli's Interest Compounding equation which is where
His formula was:
So we take yours:
and we say, let
If we rewrite it, we can use l'Hospital.
Because the exponential function is continuous,
So let's focus on the exponent
So we'll rewrite it as
Apply l'Hospital, to get the limit of the exponent is
Therefore, the limit of the original expression is
If the initial form of the limit is
Whose limit has form
Now we can try using l'Hospital's rule to find the limit of the logarithm of