$f(f(x)) = \log(x) \forall x > 0$, what is $f$?
97767
How do I construct a function $\operatorname{sog}$ such that $\operatorname{sog}\circ\operatorname{sog} = \log$?
106830
are $f(f(x))=f(x)$ and $f(x)=x$ equivalent?
72847
Does $f(x)$ is continuous and $f = 0$ a.e. imply $f=0$ everywhere?
132093
Solve $f(f(x))=f(x)$
82597
How to find $ f(x)$ if $f(1-f(x))=x$ for all $x$ $\in \mathbb{R}$
33989
If $\int_0^1 f(x)x^n \ dx=0$ for every $n$, then $f=0$.
136185
How $a^{\log_b x} = x^{\log_b a}$?
39747
Showing that $\lim_{x\to 0} x\log{x}= 0$ without using L'Hopital's rule
150991
What is the order of the sum of log x?
121237
Solving $x - a \log(x)=b$
147108
Prove that $\int_0^\infty \frac{x\,\log x}{(1+x^2)^2} = 0$
113394
What does O(log n) mean exactly?
118873
Prove that $f(x)=0$ for all $x\in\mathbb{R}$.
69008
$f'(x) = [f(x)]^{2}$. Prove $f(x) = 0 $
66406
How to calculate $f(x)$ in $f(f(x)) = e^x$?
32575
What's the name for the property of a function $f$ that means $f(f(x))=x$?
127605
What are some methods to show $\log$ is not a rational function?