Answer
True.
Work Step by Step
Applying the Product Rule: $\quad \log_{b}(MN)=\log_{b}\mathrm{M}+\log_{b}\mathrm{N}$
to the LHS,
$\log_{6}[x\cdot(x+1)]=\log_{6}x+\log_{6}(x+1)$
Thus, the statement is true.
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