Well, log[2](2x^3) = log[2](x^3) + 1 for a start, and then log[2](x^3) = 3log[2](x), so you end up with
(log[2](x))^2 + 3log[2](x) + 2
and that's another quadratic term in log[2](x), so you can find roots like in question 1 again.
I knew my degree would be useful for something...