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

We know: ln($\displaystyle x^{n}$)=n ln(x)

-> 2ln(x)=ln(2) --> ln(x)=$\displaystyle {\frac{ln(2)}{2}}$. --> x= $\displaystyle e^{\frac{ln(2)}{2}}$.

Is that correct? Because my booklet, again, says something different

2) are generally all logarithmic rules appliable for ln?