(* Definition of log R+* -> R *)
(* 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).