How do you calculate Ln(0.84)?

1 Answer
Feb 10, 2017

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