
theorem
  for a be positive non weightless Real, b be positive Real holds
  log (a,b) = 0 iff b = 1
  proof
    let a be positive non weightless Real, b be positive Real;
    A1: |.a.| <> 1 by TA1;
    log (a,b) = 0 implies b = 1
    proof
      a to_power log (a,b) = b;
      hence thesis by POWER:24;
    end;
    hence thesis by POWER:51,A1;
  end;
