In one of my older threads, I posted the following: log_b (n) = x if and only if b ^ x = n, where b > 0, and b is not equal to one. It was said this defines logarithm as the inverse to exponential. I don't really see how that works here, I think it just shows how you write logarithms. Could anyone clear this up? Also, I'm wondering something about inverses in general. Say you have a simple example like (x + 1) - 1 = x. This equation says that (x + 1), and (x - 1) are inverses, correct? Is there a way to mathematically show that? Or do you simply conclude this qualitatively? I'm thinking if it's just qualitative, you could say something like this: If (x + 1) - 1 = x, then it must be that + 1 and - 1 do opposite things to x. Thus, you can conclude that (x + 1) and (x - 1) are inverse functions, seeing as they do opposite things to x. Does that sound right? Is there I way to mathematically show this? I know that if you take (x + 1) and (x - 1) and sub one into the other you get either (x + 1) - 1 = x or (x - 1) + 1 = x, but can you do this backwards, by starting from (x + 1) - 1 = x or (x - 1) + 1 = x? Thanks in advance for any help I get.