Summary: How can old-fashioned tables of logarithms be computed without technology? Today, of course, no practicing mathematician, scientist, or engineer would actually use logarithms to carry out a calculation, let alone worry about deriving them from scratch. But high school students may be curious about the process. This article develops a straightforward technique for computing common logarithms by establishing a few successive square roots of 10. Because the logarithms of these values are by definition just the power to which 10 has been taken ($1/2$, $1/4$, $1/8$, etc.), these values can be used to construct a table of logarithms in which the increment in the logarithm is $1/2^N$, where $N$ is the number of square roots computed. By interpolating between these accurately computed points, we can build a standard log table. This method should help reinforce rules of logarithms and powers for students. (ERIC)