Answer
False.
To become true, change it to
$\displaystyle \log(x+9)-\log(x+1)=\log\frac{(x+9)}{(x+1)}$
Work Step by Step
Applying the Quotient Rule: $\displaystyle \qquad \log_{b}(\frac{M}{N})=\log_{b}\mathrm{M}-\log_{b}\mathrm{N}$,
$\displaystyle \log(x+9)-\log(x+1)=\log\frac{(x+9)}{(x+1)}\neq\frac{\log(x+9)}{\log(x+1)}$
so the statement is false.
