Solving #1

$\large x^x = 100 \\ \\ \large x log(x) = log(100) \\ \\ \large log(x) = \dfrac{2}{x}$

Now check the graph for $y = \dfrac{2}{x}$ and $y = log(x)$ .

The intersection points will give you the answer.

a more broader view...

$x\approx3.5972850235404175055$

3.598^3.598=100