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November 27, 2014

November 27, 2014

Posted by **Joan** on Monday, March 19, 2007 at 9:19pm.

Which of the following series can be used to compute ln(.8)?

a) ln(x-1) expanded about x=0

b) lnx about x=0

c) ln x in powers of (x-1)

d) ln(x-1) in powers of (x-1)

e) none of the proceding

I am confused... please help!

I am not certain any of our volunteers have expandied series of log functions in the recent past, and would likely give you misleading info. Perhaps one of the non regular math profs will drop in and help you.

The Taylor Series says:

ln(x)== ln(a) + (x-a) / a - (x-a)2 / 2a2 + (x-a)3 / 3a3 - (x-a)4 / 4a4 + ...

where a is a value for which you know ln(a)

your x=.8, then I would choose a=1

and

ln(.8)=ln(1)+(-.2)/1+(-.2)^2/2+(-.2)^3/3...

=0+a series of negative terms.

I did this for 5 terms and got -.2233866

with the real value of ln(.8)=-.22314..

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