Yes, 3 is the answer. But how do you "prove" that there is no other integer that satisfies the equation?? Can you come out with some "LOG" manupulation that shows that "3" is the only answer?
"Log" is unnecessary here.
because n is integer
n>=0, (if n<0, then (n+2)^n<=1)
(n+2) is an integer, there is no other integers' any exponent equal to 125, only 5. n+2=5 => n=3
Kudos me if my reply helps!