# How can I calculate a logarithm without a calculator?

##### 1 Answer

See explanation, where I show how to find

#### Explanation:

Since you were not specific as to what base of logarithm you wanted, I will take the liberty of showing you how to calculate logarithms base 2 in binary. They are perhaps the easiest to do by hand. Elsewhere I have shown a method to calculate common (base

Let us calculate

From now on express numbers in binary...

We want to calculate

So the digits before the binary point are

Next divide

Square

Since this is greater than

Divide by

Square

Since this is greater than

Divide by

Square

Since this is less than

Square

Since this is less than

To cut down on the arithmetic, I will approximate this as

Square

Since this is greater than

Divide by

I'll stop here, but I hope you get the idea.

Putting the digits we have found together we get:

#log_(10_2) 111_2 ~~ 10.11001_2 = 2+25/32 ~~ 2.8#

Actually