Answer
$2 \ln(2x+3)-2 \ln (x-2)-2 \ln (x-1)$
Work Step by Step
Use the log rule
$\log_a{(mn)}=\log_a{m} + \log_a{n}$
We obtain:
$\ln[\dfrac{2x+3}{(x-2)(x-1)}]^2 =2[ \ln(2x+3)-\ln (x-1)(x-2)] $
Now, use $\log_a(mn)=\log_a{m}+\log_a{n}$ to obtain:
$2[ \ln(2x+3)-[\ln (x-1)+\ln (x-2)]]=2[ \ln(2x+3)-\ln (x-1)-\ln (x-2)] \\=2 \ln(2x+3)-2 \ln (x-2)-2 \ln (x-1)$