to be fair it does seem to work for any two numbers where one is >1.
As lim x,y–> inf ln(ex+ey) <= lim x,y --> inf ln(2 e^(max(x,y))) = max(x,y) + ln(2).
I think is cool because works for any number of variables
using the same proof as before we can see that:
lim,x_i -->inf ln(sum_i/in I} e^(x_i)) <= ln(.
So it would only work for at most [base of your log, so e<3 for ln] variables.
to be fair it does seem to work for any two numbers where one is >1. As lim x,y–> inf ln(ex+ey) <= lim x,y --> inf ln(2 e^(max(x,y))) = max(x,y) + ln(2).
using the same proof as before we can see that: lim,x_i -->inf ln(sum_i/in I} e^(x_i)) <= ln(.
So it would only work for at most [base of your log, so e<3 for ln] variables.