As you say the first step is to take log of both sides after that you are just applying the rules for logarithms and rearrange.
$$\ln (XZ)=\ln X + \ln Z$$
$$\ln X/Z= \ln X - \ln Z$$
$$\ln X^a = a \ln X$$
$$\ln 1 = 0$$
Also an important approximations that hold close to zero are applied here as well these are:
$\ln(1+x) \approx x $ for $x$ ...