How To Male A Log Table: A Flagrant Exercise In Atavism

Imagine that you're stranded on a desert island and want to make a table of logarithms.Why, for heaven's sakes? That's obviously silly. Even sillier: In discussing this problem, we will do a lot of computation, both arithmetic, algebraic, and statistical, and such computations are of course best done on a calculator. But if you have a calculator, wanting a log table is even more absurd.There are probably both log10 and ln buttons on the calculator, with more accuracy than we will ever achieve here!

The excuse is that it's a nice problem. If you're someone to whom mathematics can be fun, this is fun. It ties together many different aspects of mathematics, and a fair amount of it could be done in middle school if one really wanted to. So let's make our problem specific. We would like values for the logs to the base 10 of the integers from 1 to 10. What can we use? We assume knowledge of the basic properties of logarithms, we expect that larger numbers will have larger logarithms, and that nearby numbers will have nearby logarithms.