Write ln(x-4)-5 ln(2x+7) - 1/2 ln(3x+1) + 6 ln(x) as a single logarithm
Start by rewriting any term with a coefficient as a term with a power inside the logarithm (using the rule $\displaystyle p\log{a} = \log{(a^p)}$).
You should then be able to simplify the rest using the sum/difference rules $\displaystyle \log{a} + \log{b} = \log{(ab)}$ and $\displaystyle \displaystyle \log{a} - \log{b} = \log{\left(\frac{a}{b}\right)}$.