$x^{x}$ as a composite function

Question

I understand that this question has been asked a lot of times but I haven't yet got a clear explanation $$x^{x}$$ is not called a composite function.

The reason they give is that it cant be written as $$f(g(x))$$ and then they start talking about logarithms

What I want to know is that why it cant be written as a composite function with some examples without involving logarithms in the explanation

Just a clear reason with example

Answer 1

We can write $x^x = e^{x\ln(x)}$ for $x>0$. In this way, it is a composite function.