If R^a = R^b, for what values of R can we say that a=b?

Rajesh,

I'm assuming that R is an integer.

Generally, my understanding would be that a = b in every case except 0 or 1 (where either raised to any power would be equal to 0 or 1) or -1 (where a and b can be different and the result is still 1 or -1).

For all other integers as R, a would equal b.

I hope that this is helpful. Let me know if it is consistent with your understanding, or if you have any specific follow-ups. - Andrew

Thanks for the reply. My understanding is the same. I got confused when I saw "Since R<>0, a=b" many times even in books. That left me thinking R could be 1 also and that means a may not be equal to b.