How do you calculate #Ln(0.84)#?

1 Answer
Feb 10, 2017

Answer:

#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#