Does anyone know how to formally prove that 3^n has a higher growth rate than c*2^n? In other words no matter how large c is, you can always find some natural number n that makes 3^n larger? It's quite obvious this is true but I don't know the steps to proving it. I used L'Hopital's rule in comparing these two as n -> ∞, but don't know how to isolate the n so that one side has n and the other has c.

Thanks.