Answer
True
Work Step by Step
Applying the Product Rule:
$\log_{\mathrm{b}}(\mathrm{M}\mathrm{N})=\log_{\mathrm{b}}\mathrm{M}+\log_{\mathrm{b}}\mathrm{N}$,
LHS= $\log_{6}[4\cdot(x+1)]=\log_{6}4+\log_{6}(x+1),$
which equals the RHS of the problem statement.
So, the problem statement is true.