Thread: How do I prove b^x * b^y = b ^ x + y on R?

How do I prove b^x * b^y = b ^ x + y where b > 1 and x, y are on R?

Originally Posted by pDeCrunch

How do I prove b^x * b^y = b ^ x + y where b > 1 and x, y are on R?

Look at how is defined for , you will find it is defined as a limit of rational powers. Now look at how you might define .

CB

Originally Posted by CaptainBlack

Look at how is defined for , you will find it is defined as a limit of rational powers. Now look at how you might define .

CB

Is it sufficient to say that x <= a, y <= b (supremum) then x + y <= a + b
so b ^ x + y <= b ^ a + b, how do I proceed to make the >= argument so that I can wedge them and make an equivalence relation.