Need Aproximate expressions for : ln(x) and 1/ln(x) Thanks

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The forum discussion focuses on finding approximate expressions for the functions ln(x) and 1/ln(x). A key suggestion is to utilize Taylor expansions, particularly around values other than x=0, due to the non-analytic nature of ln(x) at that point. The discussion highlights the use of the series for ln((1+x)/(1-x) to derive approximations for ln(x) within the interval -1 PREREQUISITES

  • Understanding of Taylor series expansions
  • Familiarity with logarithmic functions
  • Knowledge of analytic functions
  • Basic calculus concepts
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Boudy
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Hi there:
I am looking for approximate expressions for the two functions: ln(x) and 1/ln(x) . Any help?
Thanks in advance.
 
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Approximations where, for what? Did you try Taylor expansions?
 
ln(x) is not analytic at x=0. You need to use a series around some other value. If you use the series for ln((1+x)/(1-x)) you will able to get a series for any y=(1+x)/(1-x) for -1<x<1.
 

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