How do I simplify $\mathrm{log}(1/\sqrt{1000})$?

What I have done so far:

1) Used the difference property of logarithms

$\mathrm{log}\left({\displaystyle \frac{1}{\sqrt{1000}}}\right)=\mathrm{log}(1)-\mathrm{log}(\sqrt{1000})$

2) Used the exponent rule for logarithm

$\mathrm{log}(1)-\frac{1}{2}\mathrm{log}(1000)$

I'm stuck at this point. Can someone explain why and what I must do to solve this equation?

What I have done so far:

1) Used the difference property of logarithms

$\mathrm{log}\left({\displaystyle \frac{1}{\sqrt{1000}}}\right)=\mathrm{log}(1)-\mathrm{log}(\sqrt{1000})$

2) Used the exponent rule for logarithm

$\mathrm{log}(1)-\frac{1}{2}\mathrm{log}(1000)$

I'm stuck at this point. Can someone explain why and what I must do to solve this equation?