... you firmly grasp your slide rule (its plastic is comfortingly warm).
You take the logs of the two numbers with swift aplomb note them down with your trusty crayon on the SO's thigh (first available place to scribe) and without wavering, you add them together.
Armed with the crucial sum you deliver the answer to the multiplication with a casual flick and a careful read of the slide rule.
Yes, we have progressed somewhat. However, there is something rather satisfying using a slide rule. You do somehow feel the numbers within your hands. With a slide rule you can deal with far bigger numbers than you feel comfortable within your noddle (head). You can do that too with a calculator but you "feel and touch" the numbers with a slide rule.