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