what are the domains of y=ln(x^2-4x)
The domain of y=f(x) is the range of values of x such that f(x) exists.
We know that the ln() function does not admit negative arguments, so the domain of f(x) consist of the ranges of x which makes x^2-4x non-negative, or
x^2-4x≥0 .... (1)
The solution to equation (1) is the domain of f(x).
If you are not sure what to do, plot g(x)=x^2-4x and the parts of the curve that is above the x-axis correspond to the values of the domain. The domain in this case consists of two disjoint intervals.