reserve n for Nat,
  i for Integer,
  p, x, x0, y for Real,
  q for Rational,
  f for PartFunc of REAL,REAL;

theorem Th12:
  log(number_e,exp_R(x)) = x
proof
  exp_R(x) > 0 & number_e to_power x =exp_R(x) by Th9,SIN_COS:55;
  hence thesis by Lm4,POWER:def 3;
end;
