Answer
False,
$\displaystyle \log(x+3)-\log(2x)=\log(\frac{x+3}{2x})$
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=$\displaystyle \log(x+3)-\log(2x)=\log(\frac{x+3}{2x})$,
which does not equal the RHS of the problem statement.
(There is no rule to expand a quotient OF logarithms, which is what we have there)
So, the statement is false.
To make it true, change the RHS to $\displaystyle \log(\frac{x+3}{2x})$.
