One of the best mathematical tools ever developed is the of a number. It has been used extensively in the past for the simplification of lengthy arithmetic calculations. The standard way of using the technique is via tables of common logarithms. is well known and has been in use for decades. In this article, we will talk about a lesser known method of finding log of a number using the tables. logarithm The method of using these tables without Things to memorize We choose to work with base 10 log(2) ≈ 0.301 log(3) ≈ 0.477 log(5) ≈ 0.699 log(7) ≈ 0.845 Master Formula Here, and are such that ∣ − ∣ is as small as possible and is chosen according to the list above. The accuracy of the result depends on smallness of ∣ − ∣. a b a b b a b Let us try to evaluate the value of log(2.7). So, we have = 2.7 and we choose = 2.8. We can plug these values in the master formula to get a b The values of log(2) and log(7) are already known(memorized!) from the list above, so we have The exact value of log(2.7) = 0.4314 and the error in the result is just 0.03% For numbers less than 2, multiply and divide with an appropriate factor to bring it close to 5 or 7 in order to minimize errors. For e.g. Now, the master formula can be used as before. This article was originally published at https://physicsgarage.com
