Please don't be scared when you see this.

The problem asks me to expand the following logarithm into sums and differences of logarithms whose arguments are as simple as possible:

log[((√x^{2}-1)(x^{2}-x)x^{3})/(x(x-2)10^{4})]

This is what I did:

= log(√x^{2}-1)+log(x^{2}-x)+3log(x)-log(x)+log(x-2)+log(10^{4})

= log(√x^{2}-1)+log(x^{2}-x)+3log(x)-log(x)+log(x-2)+4log(10) as final answer

Not sure if this is correct or if I followed the steps correctly. Would appreciate if someone would look over this and tell me if I did it right.