## College Algebra (6th Edition)

False, $\displaystyle \log(x+3)-\log(2x)=\log(\frac{x+3}{2x})$
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 $\displaystyle \log(\frac{x+3}{2x})$.