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

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The discussion revolves around finding a function f such that f(f(x)) equals log_a(x), which could help extend the definition of superlogarithms. Participants explore the idea of defining log_a(x) based on repeated divisions by a constant until reaching 1, and suggest that functions like f(x) = x/a^(1/n) could be useful. There is debate on the clarity and precision of the proposed methods, with some arguing that intuitive approaches lack the rigor needed for mathematical acceptance. The conversation highlights the importance of formal definitions and proofs in mathematical discourse, especially when introducing new concepts. Overall, the thread emphasizes the need for precise algorithms to validate the proposed extensions of logarithmic functions.
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