To find the logarithm of a quotient like 3/5840 using a logarithmic table, first express the numbers in scientific notation. The logarithm of a product can be calculated using the formula log(AB) = log(A) + log(B), while the logarithm of a quotient uses log(A/B) = log(A) - log(B). The discussion references a logarithmic table similar to those found in CRC series books, which typically contain logs for values from 0.100 to 0.999. Users are encouraged to consult old Intermediate Algebra textbooks for detailed instructions on using log tables. Understanding the concepts of logarithm, base, and anti-logarithm is essential for mastering this technique.