How do calculators calculate logarithms?

Answer 1

As far as I am aware there is no formula as such to calculate log. The definition of a log is n = Blog n , where n is the number being logged and B is the base to which it is being logged. This means, log n is the power to which B must be raised to give n.

It's not difficult to estimate once you decide what B is. If you choose base 10, which is what we count in usually, the first number in the log is the highest power of 10 which is lower than the number. If the number is 5000 then the 1st number in the log will be 3, as 103 = 1000 . log 5000 will be more than 3, less than 4.

You can work out approximate values for log n by plotting a graph on ordinary graph paper. If you plot 0 to 10 across and 0 to 1 up the side, then put in the two points properly known (where n=1, log1=0 and for n=10, log10=1). Easily memorable are log of 2, 4, annd 8 which are very close to 0.3, 0.6 and 0.9, but those came straight out of my calculator.

ANSWER:

There are several ways to calculate logarithms. Euler could calculate logarithms using a binary search and the geometric mean. There is another way to calculate the log using the natural logarithm, base e. I developed my own method using squares, and there is a link provided.

Answer 2

the working of calculaters based on some logic gates that are or,and,nor gates the log functions are coded by some gates