How do I simplify $\log (1/\sqrt{1000})$? How do I simplify $\log \left(\displaystyle\frac{1}{\sqrt{1000}}\right)$?
What I have done so far: 
1) Used the difference property of logarithms 
$$\log \left(\displaystyle\frac{1}{\sqrt{1000}}\right) = \log(1) - \log(\sqrt{1000}) $$
2) Used the exponent rule for logarithm 
$$\log (1) - \frac{1}{2}\log (1000) $$
I'm stuck at this point. Can someone explain why and what I must do to solve this equation? 

Hint:
$$\frac{1}{\sqrt{1000}}=10^{-\frac{3}{2}}\qquad\mbox{and}\qquad\log x^a=a\log x$$
