Answer
$\log_{2} \frac{x^{5}}{(x-1)^{2}}$
Work Step by Step
$2\log_{2} x+3\log_{2} x-2\log_{2} (x-1)$
=$\log_{2} x^{2}+\log_{2} x^{3}-\log_{2} (x-1)^{2}$
=$(\log_{2} x^{2}+\log_{2} x^{3})-\log_{2} (x-1)^{2}$
=$\log_{2} (x^{2} \times x^{3})-\log_{2} (x-1)^{2}$
=$\log_{2} (x^{5})-\log_{2} (x-1)^{2}$
=$\log_{2} \frac{x^{5}}{(x-1)^{2}}$
