Mathematically, log(x/(y*z)) and log(x)-log(y)-log(z) are equivalent. On a computer, they will give different answers. Which is preferable to compute?
Log is numerical stable but division not so. Imagine y and z are very close to 0. Then y * z has a great probability to be evaluated to 0 and x / (y * z) to overflow. But log(y) even for very small y gives accurate results. So log(x)-log(y)-log(z) is expected to be more precise.