The solution x = -1 is indeed correct. Not sure why you think the first log is "impossible" for x = -1. Make the substitution for the left hand side and you get:

log(2x-2)^2 = log(2(-1)-2)^2 = log(-4^2) = log 16. Note that log(-4^2) is NOT the same as 2 log(-4).

For the right hand side: 4 log(1-x) = 4 log(2) = log 16.