exponentiation - Exponents with variables inside exponents

I am confused about how to reduce this, is there any way?

$\sqrt x \ln(\sqrt x) = ln(\sqrt x^\sqrt x) = $ $?$

This can be written like this too:

$ln(x^\frac{x^\frac{1}{2}}{2}$)

Or:

$ln(x^\frac{\sqrt x}{2}$)