Does a functional square root of a logarithm exist? [closed]

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Is there a function $f$, such that $f(f(x)) = ln(x)$?




logarithms




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closed as off-topic by Holo, Xander Henderson, Did, amWhy, TheSimpliFire Aug 17 at 18:41


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Holo, Xander Henderson, Did, amWhy, TheSimpliFire
If this question can be reworded to fit the rules in the help center, please edit the question.








  • 1




    Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. This should be added to the question rather than in the comments.
    – José Carlos Santos
    Aug 17 at 8:24










  • Any additional assumptions on $f$, such as continuity or differentiability?
    – Sobi
    Aug 17 at 8:26










  • What would be the domain and range of $f$?
    – A. Pongrácz
    Aug 17 at 8:28






  • 6




    If $f$ is invertible, its inverse is the "half exponential", such that $g(g(x))=e^x$. en.wikipedia.org/wiki/Half-exponential_function
    – Yves Daoust
    Aug 17 at 8:28






  • 1




    Do you have reason to suspect that there is such a function $f$? Like, what's your motivation for asking this question?
    – Mike Pierce
    Aug 17 at 18:29















up vote
4
down vote

favorite
3












Is there a function $f$, such that $f(f(x)) = ln(x)$?




logarithms




share|cite|improve this question












closed as off-topic by Holo, Xander Henderson, Did, amWhy, TheSimpliFire Aug 17 at 18:41


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Holo, Xander Henderson, Did, amWhy, TheSimpliFire
If this question can be reworded to fit the rules in the help center, please edit the question.








  • 1




    Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. This should be added to the question rather than in the comments.
    – José Carlos Santos
    Aug 17 at 8:24










  • Any additional assumptions on $f$, such as continuity or differentiability?
    – Sobi
    Aug 17 at 8:26










  • What would be the domain and range of $f$?
    – A. Pongrácz
    Aug 17 at 8:28






  • 6




    If $f$ is invertible, its inverse is the "half exponential", such that $g(g(x))=e^x$. en.wikipedia.org/wiki/Half-exponential_function
    – Yves Daoust
    Aug 17 at 8:28






  • 1




    Do you have reason to suspect that there is such a function $f$? Like, what's your motivation for asking this question?
    – Mike Pierce
    Aug 17 at 18:29













up vote
4
down vote

favorite
3









up vote
4
down vote

favorite
3






3





Is there a function $f$, such that $f(f(x)) = ln(x)$?




logarithms




share|cite|improve this question












Is there a function $f$, such that $f(f(x)) = ln(x)$?





logarithms





share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Aug 17 at 8:19









Zeick

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1304




closed as off-topic by Holo, Xander Henderson, Did, amWhy, TheSimpliFire Aug 17 at 18:41


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Holo, Xander Henderson, Did, amWhy, TheSimpliFire
If this question can be reworded to fit the rules in the help center, please edit the question.




closed as off-topic by Holo, Xander Henderson, Did, amWhy, TheSimpliFire Aug 17 at 18:41


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Holo, Xander Henderson, Did, amWhy, TheSimpliFire
If this question can be reworded to fit the rules in the help center, please edit the question.







  • 1




    Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. This should be added to the question rather than in the comments.
    – José Carlos Santos
    Aug 17 at 8:24










  • Any additional assumptions on $f$, such as continuity or differentiability?
    – Sobi
    Aug 17 at 8:26










  • What would be the domain and range of $f$?
    – A. Pongrácz
    Aug 17 at 8:28






  • 6




    If $f$ is invertible, its inverse is the "half exponential", such that $g(g(x))=e^x$. en.wikipedia.org/wiki/Half-exponential_function
    – Yves Daoust
    Aug 17 at 8:28






  • 1




    Do you have reason to suspect that there is such a function $f$? Like, what's your motivation for asking this question?
    – Mike Pierce
    Aug 17 at 18:29













  • 1




    Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. This should be added to the question rather than in the comments.
    – José Carlos Santos
    Aug 17 at 8:24










  • Any additional assumptions on $f$, such as continuity or differentiability?
    – Sobi
    Aug 17 at 8:26










  • What would be the domain and range of $f$?
    – A. Pongrácz
    Aug 17 at 8:28






  • 6




    If $f$ is invertible, its inverse is the "half exponential", such that $g(g(x))=e^x$. en.wikipedia.org/wiki/Half-exponential_function
    – Yves Daoust
    Aug 17 at 8:28






  • 1




    Do you have reason to suspect that there is such a function $f$? Like, what's your motivation for asking this question?
    – Mike Pierce
    Aug 17 at 18:29








1




1




Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. This should be added to the question rather than in the comments.
– José Carlos Santos
Aug 17 at 8:24




Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. This should be added to the question rather than in the comments.
– José Carlos Santos
Aug 17 at 8:24












Any additional assumptions on $f$, such as continuity or differentiability?
– Sobi
Aug 17 at 8:26




Any additional assumptions on $f$, such as continuity or differentiability?
– Sobi
Aug 17 at 8:26












What would be the domain and range of $f$?
– A. Pongrácz
Aug 17 at 8:28




What would be the domain and range of $f$?
– A. Pongrácz
Aug 17 at 8:28




6




6




If $f$ is invertible, its inverse is the "half exponential", such that $g(g(x))=e^x$. en.wikipedia.org/wiki/Half-exponential_function
– Yves Daoust
Aug 17 at 8:28




If $f$ is invertible, its inverse is the "half exponential", such that $g(g(x))=e^x$. en.wikipedia.org/wiki/Half-exponential_function
– Yves Daoust
Aug 17 at 8:28




1




1




Do you have reason to suspect that there is such a function $f$? Like, what's your motivation for asking this question?
– Mike Pierce
Aug 17 at 18:29





Do you have reason to suspect that there is such a function $f$? Like, what's your motivation for asking this question?
– Mike Pierce
Aug 17 at 18:29
















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