Finding a Maclaurin series for ln(x)

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SUMMARY

The discussion centers on finding a Maclaurin series for ln(x), specifically for calculating ln(1.5). Since ln(0) is undefined, the focus shifts to using the Maclaurin series for ln(1 + x) to evaluate ln(1.5) by substituting x = 0.5. Participants suggest that using the Taylor series for ln(x) around x=1 is also a viable option, but recommend confirming the approach with the instructor for clarity.

PREREQUISITES
  • Understanding of Maclaurin series and Taylor series
  • Familiarity with logarithmic functions, specifically ln(x)
  • Basic calculus concepts, including series expansion
  • Knowledge of function substitution in series
NEXT STEPS
  • Research the derivation of the Maclaurin series for ln(1 + x)
  • Study the Taylor series expansion for ln(x) around x=1
  • Practice evaluating series convergence for logarithmic functions
  • Explore numerical methods for approximating logarithmic values
USEFUL FOR

Students in calculus courses, mathematics educators, and anyone interested in series expansions and logarithmic function approximations.

bobber205
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Since ln(0) doesn't exist, this question is futile right?

I am tasked with finding a Maclaurin powerseries for ln(x) and to find out how many times I have to run that series to get a accurate answer for ln(1.5).

What should I do? Should I find the taylor series for ln(1.5) for should I find the Maclaurin for ln(1 + x) and find out what .5 is instead of 1.5.

Thanks.
 
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Should I find the taylor series for ln(1.5) for should I find the Maclaurin for ln(1 + x) and find out what .5 is instead of 1.5.

Seems like the better choice (Maclaurin for ln(1 + x) or Taylor of ln(x) about x=1) - this may be what was intended all along. However, you should clarify with instructor.
 

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