Logarithmic Factorization and Representation as Power of e

Question

In some online math solution provider engines, sometimes equations are provided in a way which may be reducible to more understandable equations. Yet, they assume you know the concept in detail and shorten their solutions. My question regarding with that will be; how is the following equation possible, would you elaborate?

n^(logn)=e^((logn)^2) 

Answer 1

we have $$\log(n)\log(n)=(\log(n))^2$$ and it is $$x^{\alpha}=e^{\alpha\ln(x)}$$ for $x>0$

Answer 2

According to our little exchange in the comments, you know that $e^{\ln n}=n$. This and $\left(a^b\right)^c=a^{bc}$ are the key propertis to prove the given identity: $$n^{\ln n}=\left(e^{\ln n}\right)^{\ln n}=e^{(\ln n)^2}.$$