Can you draw a logarithmic scale just using some clever geometric construction? Or can it only be done using an actual table of logarithms? (It's obviously trivial to draw a linear scale. It isn't hard to draw a scale where the spaces between tick marks doubles at each step. But I can't think of a way to get a logarithmic scale.)
I'm not especially worried about exactly which operations are permitted. I'm really just interested in whether you can make a slide rule without doing a bunch of pencil and paper calculations first...