I guess there's no way to convert a^x to E^(x*Log[a]) and keep it in that form? It should be a way that newbie student users can manage. I want them to see the argument(s) of the exponential function(s) in an equation.
@MichaelE2 The leaf count is same, which is 3. So simplify and FullSimplify will not work. Reduce knows they are the same. Reduce[a^x == Exp[x*Log[a]]] gives True. Looks like special rule is needed and nothing builtin.
@Nasser What I mean is that E^(x*Log[a]) autosimplifies to a^x unless it is held. In another case, Log[a, x] autosimplifies to Log[x]/Log[a], but you can turn that off with a system option. I don't know of a similar thing with Power[]. I can manage with HoldForm or Defer, but I doubt my students could. Thanks.
@MichaelE2 yes, I saw that before, i.e. Simplify[E^(x*Log[a])] gives a^x. I thought it was strange since leaf count is same. Mathematica must have this hardcoded or there is another metric used. If you have Maple, it does it using one of its special convert function, like this
convert(a^x,exp) which gives what you wanted.. Screen shot below
