I am not sure how to work these two kinds of problems out:

1) Solve this equation:

log2 (x-3)(x+1)=5

I keep getting x= 4 or x=-2 but the solution says that the answer is -5, 7. Could someone inform me where I have made a mistake?

log2 (x-3)(x+1)=5

log2 x^2-2x-3=5

log2 x^2-2x-8=0

log2 (x-1)^2-9

log2 (x-1+3)(x-1-3)

log2 (x+2)(x-4)

x=-2, x=4

2)Find the domain of the following:

1/log2 (x^2-6x+8)

I'm not quite sure how to even go about this one.

Thank you.