2logₐx- 3logₐ2x + 2logₐx²

assuming base a, that would b

log(x^2+ (x^2)^2 / (2x)^3) = -log8 or -3log2

2logₐx- 3logₐ2x + 2logₐx²

= logₐ(x^2) - logₐ(8x^3) + logₐ(x^4)
= logₐ (x^6 /(8x^3))
= logₐ (x^3 / 8)
= 3logₐ x - logₐ 8