Answer
$=\log \dfrac {\left( x+2\right) }{\left( x+1\right) }$
Work Step by Step
We use the rules of logarithms to obtain:
$\log \left( x^{2}+3x+2\right) -2\log \left( x+1\right) =\log \left( x^{2}+3x+2\right) -\log \left( x+1\right) ^{2}=\log \dfrac {\left( x^{2}+3x+2\right) }{\left( x+1\right) ^{2}}=\log \dfrac {\left( x+1\right) \left( x+2\right) }{\left( x+1\right) ^{2}}=\log \dfrac {\left( x+2\right) }{\left( x+1\right) }$
