Question

How do you calculate `Ln(0.84)`?

Answer 1

`ln(0.84) ~~ -0.1743`

Explanation:

Let us start with:

`ln(1+x) = x/1-x^2/2+x^3/3-x^4/4+...`

Hence:

`ln(1-x) = -x/1-x^2/2-x^3/3-x^4/4-...`

Putting `x=0.16` we find:

`ln(0.84) = ln(1-0.16)`

`color(white)(ln(0.84)) = -0.16/1-0.16^2/2-0.16^3/3-0.16^4/4-...`

`color(white)(ln(0.84)) = -0.16/1-0.0256/2-0.004096/3-0.00065536/4-...`

`color(white)(ln(0.84)) = -0.16-0.0128-0.001365bar(3)-0.00016384-...`

`color(white)(ln(0.84)) ~~ -0.1743`