(* Definition of log R+* -> R *)
Definition Rln (y:posreal) : R :=
  let (a,_) := ln_exists (pos y) (cond_pos y) in a.(* Extension on R *)
Definition ln (x:R) : R :=
  match Rlt_dec 0 x with
    | left a => Rln (mkposreal x a)
    | right a => 0
  end.Definition Rlog x y := (ln y)/(ln x).

Lemma ln_pow : forall (x : R), 0 < x -> forall (n : nat), ln (x^n) = (INR n)*(ln x).