Answer
True
Work Step by Step
Applying the Quotient Rule:
$\displaystyle \log_{\mathrm{b}}(\frac{\mathrm{M}}{\mathrm{N}})=\log_{\mathrm{b}}\mathrm{M}-\log_{\mathrm{b}}\mathrm{N}$,
LHS=$\displaystyle \log_{6}(\frac{x-1}{x^{2}+4})=\log_{6}(x-1)-\log_{6}(x^{2}+4),$
which equals the RHS of the problem statement.
So, the problem statement is true.