Why is $x^2\ln\sqrt{x}$ equal to $\frac{x^2}{2}\ln x$? My textbook jumps from $$x^2\ln\sqrt{x}$$
to
$$\frac{x^2}{2}\ln x$$
What intermediate steps occur?

Properties of logarithm 
$$\log(x^a) = a\log(x)$$
Thence
$$\log(\sqrt{x}) = \log(x^{1/2}) = \frac{1}{2}\log(x)$$
