Answer
True.
Work Step by Step
$\log_{a}(Q+Q^{2})=\qquad$ ... rewrite $Q+Q^{2}$ as $Q(1+Q)$
$=\log_{a}[Q(1+Q)]\qquad$ ... apply $\log_{a}(MN)=\log_{a}M+\log_{a}N$
$=\log_{a}Q+\log_{a}(Q+1)$
True.
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