Hmmmm...
I would hate to challange the learned AC K, as his 'Mechanics of Flight' is the basic repository for most aviation knowledge. BUT...
As the density of air at FL390 at -56 is NOT the same as the density at FL450 at -56, I think that we all agree. However, we all agree that the LSS is equal at both atltitudes, by the formula.
Has the basic formula been simplified for the 'not so clever guys that drive the buses'?