How to mix and match log rules?

Question

I know that $\ln(xy) = \ln(x) + \ln(y)$, that $\ln(\frac{x}{y}) = \ln(x) - \ln(y)$ and that $\ln(\sqrt{x}) = \frac{1}{2}\ln(x) = \frac{\ln(x)}{2}$ but I can't seem to find any rules for more complex things such as $\ln(\frac{x}{y\sqrt{z}})$.

Does $\ln(\frac{x}{y\sqrt{z}}) = \ln(x) - \ln(y) + \frac{\ln(z)}{2}$ or does $\ln(\frac{x}{y\sqrt{z}}) = \ln(x) - \frac{\ln(z)}{2} + \ln(y)$ or something else? How can I tell what order the logs go in? Does it matter?

Answer 1

$\ln(\frac{x}{y\sqrt{z}}) = \ln(x) - \ln(y\sqrt{z}) = \ln(x) - \ln(y) -\ln(z^{1/2})= \ln(x) - \ln(y) - \ln(z)/2. $

Answer 2

Think $$ \ln \left( \frac{ab}{cd}\right) = \ln( ab(1/c)(1/d)) = \ln(a)+\ln(b)+\ln(1/c)+\ln(1/d). $$