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General Discussion => Other Discussions => Math and Science => Topic started by: aeTIos on December 23, 2011, 09:09:29 am

Title: calculating the natural logarithm of an arbitrary number
Post by: aeTIos on December 23, 2011, 09:09:29 am

Hello guys,

As stated in the subject. I can't use this: (http://mathworld.wolfram.com/images/equations/MercatorSeries/Inline3.gif) since that only works for x=-1 through x=1...

Who knows another summation/computation algorithm? Thanks!

Title: Re: calculating the natural logarithm of an arbitrary number
Post by: bsl on December 23, 2011, 09:52:03 am

Quote from: aeTIos on December 23, 2011, 09:09:29 am

Hello guys,

As stated in the subject. I can't use this: (http://mathworld.wolfram.com/images/equations/MercatorSeries/Inline3.gif) since that only works for x=-1 through x=1...

Who knows another summation/computation algorithm? Thanks!

(x-1)/(x+1) +1/3 * [(x-1)/(x+1)]^3 + 1/5 * [(x-1)/(x+1)]^5 + 1/7 * [(x-1)/(x+1)]^7 .....
for x > 0
There are shortcuts on a calculator to do this.

Title: Re: calculating the natural logarithm of an arbitrary number
Post by: Adriweb on December 23, 2011, 12:52:44 pm

Taylor it :)


(oh, well, bsl actually wrote directly an approximation...)

Title: Re: calculating the natural logarithm of an arbitrary number
Post by: phenomist on January 18, 2012, 02:31:34 am

Also, ln(x)=-ln(1/x)

If x is not between -1 and 1, take its reciprocal. (I'd also like to note that ln(negative number) is a bad idea.)