When I graphed the relation $a^{a+2b}=b^{b+2a}$ , it gives a graph similar to $y=x$. However, the question explicitly states that $a \neq b$. So does that mean that no such $N$ exists ?
What happens when the problem is generalized as $N=a^{ma+nb}=b^{mb+na} $ ?
Can anybody help as to what should be done ?
Thanks in advance :) .