How are these three equations that are rewritten equal eachother? 
This question has been driving me insane for about a day now. I cannot figure how these two are equal and I understand the laws of logarithms decently. Regardless, when I try to show equality in a calculator between these three functions expressed in the gray; I get different answers every time. So does this boil down a calculation error on my end or is there more going on here that I can't seem to wrap my head around.

The fact that in the image they are appearing equal is a bit of a misrepresentation for me. Following the help of @Bernard the equation actually is not e^(log(x))*(log(x)) but more rather x^log(x) = e^(log(x) * ln(x)) due to the base e. 
