Richard P. Feynman was once noted for being able to out-perform a mechanical calculator salesman in computation by employing logarithmic arithmetic. The first step to being able to do this effectively is to recognize that a logarithm is a measure of magnitude. With this in mind, sale we can recognize that multiplication and division of numbers refers to addition and subtraction in logarithm space. The next step is recognizing how to find logarithms without having to carry around logarithm tables. The method that I find useful involves memorizing the logarithm (I chose base 10) of the first ten or so primes, orthopedist
and then factoring the number that I need to operate on into primes in my head.
log(9) = log(3^2) = 2*log(3)
log(0.125) = log(1/8) = log(1/(2^3)) = log(1) – 3*log(2) = -3*log(2)
Once the number is represented as a power of the base, standard logarithmic arithmetic applies and most mathematical operations become pretty easy to do. Finally, converting the result into something useful is a matter of breaking up the result into known inverse logarithms and adding them up in the end. Give this a try next time someone tries to sell you a mechanical calculator, as long as it’s not a Curta.
( exp_and_log_rules.pdf )