Explanation

Note: the options render 'log₂3' as 'log(3/2)'. Taking logs base 2: x+2 + (3x/(x−1))·log₂3 = 2·log₂3. Multiplying by (x−1) gives x²+(1+log₂3)x+2(log₂3−1) = 0. One root is x = −2 (check: 2⁰·27^{2/3} = 9 ✓), and by product of roots the other is (2log₂3−2)/(−2) = 1−log₂3. So the roots are −2 and 1−log₂3 (option C).