program logaritm;

function macht(x : double; n : integer) : double;
var
  m : integer;
  p, y : double;
begin
  m := n;
  y := x;
  p := 1;
  while m > 0 do begin
    if (m and 1) > 0 then p := p * y;
    m := m shr 1;
    y := y * y;
  end;
  macht := p;
end;

procedure test;
{
  Just a Test
}
var
  M, k : integer;
  delta, onder, boven, x : double;
begin
  M := 1000;
  delta := exp(1/M*ln(10))-1;
  onder := (1/(1+delta/2))*delta*M;
  boven := (1/(1+delta)+1)/2*delta*M;
  Writeln(onder,' < ',ln(10),' < ',boven);

  delta := 1.E-3;
  onder := (1/(1+delta/2))*delta*M;
  boven := (1/(1+delta)+1)/2*delta*M;
  x := macht(1+delta,M);
  Writeln(x);
  Writeln(onder,' < ',ln(x),' < ',boven);

  delta := 2;
  M := 1;
  for k := 1 to 5 do
  begin
    delta := sqrt(delta);
    M := M * 2;
  end;
  delta := delta - 1;
  onder := (1/(1+delta/2))*delta*M;
  boven := (1/(1+delta)+1)/2*delta*M;
  x := macht(1+delta,M);
  Writeln(delta,' ',M,' ',x);
  Writeln(onder,' < ',ln(x),' < ',boven);
end;

begin
  test;
end.