Calculating limit - how to arrive at the answer ?

Questions
1

Limit[-3 x + 3 Log[-1 + E^x], x → Infinity]
How can the answer 0 be found ? (Log is natural logarithm)

2

Quite easy to explain in simple words:

-1+E^x tends to E^x for large x. So Log[E^x] = x for large x, what you are left with is -3x + 3x = 0

3

Quite easy to explain in simple words:

-1+E^x tends to E^x for large x. So Log[E^x] = x for large x, what you are left with is -3x + 3x = 0

4

Thanks !