Find ##f(x)## such that f(f(x))=##log_ax##

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    functions logarithms
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SUMMARY

The discussion centers on finding a function ##f(x)## such that ##f(f(x)) = \log_a x##, which is crucial for extending the definition of superlogarithms. Participants propose using functions like ##f(x) = \frac{x}{a^{\frac{1}{2}}}## and ##g(x) = \frac{x}{a^{\frac{1}{3}}}## to approximate logarithmic calculations. The conversation highlights the need for precise definitions and algorithms to validate these concepts mathematically. Key examples include calculating ##\log_2 20## and ##\log_4 6##, demonstrating the iterative division approach to logarithmic approximation.

PREREQUISITES
  • Understanding of logarithmic functions and their properties
  • Familiarity with Taylor series and polynomial approximations
  • Basic knowledge of iterative algorithms and numerical methods
  • Concept of superlogarithms and their mathematical significance
NEXT STEPS
  • Research the properties of superlogarithms and their applications
  • Explore Taylor series expansions for logarithmic functions
  • Study iterative algorithms for numerical approximation of functions
  • Investigate existing literature on function composition and approximation techniques
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Mathematicians, computer scientists, and students interested in advanced logarithmic functions, numerical methods, and algorithm development.

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