 reserve n,m,i,p for Nat,
         h,k,r,r1,r2,x,x0,x1,x2,x3 for Real;
 reserve f,f1,f2,g for Function of REAL,REAL;

theorem Th3:
  x>0 implies log(number_e,x) = ln.x
proof
  assume
A1: x>0;
  x in right_open_halfline(0)
  proof
    x in {g where g is Real: 0<g} by A1;
    hence thesis by XXREAL_1:230;
  end;
  hence thesis by TAYLOR_1:def 2;
end;
