Here is the following question, I am currently working on:

> 
> $$x^x = 2^{2048}$$
> Find the value of $x$.
> 
> 
> 

I decided to start by letting $x = 2^n$, where $n \in \mathbb{R}$.

Then I used index laws:

* ${2^n}^{(2^n)}=2^{2048}$
* $2^n = 2^{(2^{11-n})}$

Finally acquiring:

* $n=2^{11-n}$
* $n^{\frac{1}{11-n}} = 2$

That is where I have been able to get so far. Anyone has ideas to progress further from here?