# Math Help - Writing as a single logarithm?

1. ## Writing as a single logarithm?

Write ln(x-4)-5 ln(2x+7) - 1/2 ln(3x+1) + 6 ln(x) as a single logarithm

2. Start by rewriting any term with a coefficient as a term with a power inside the logarithm (using the rule $p\log{a} = \log{(a^p)}$).

You should then be able to simplify the rest using the sum/difference rules $\log{a} + \log{b} = \log{(ab)}$ and $\displaystyle \log{a} - \log{b} = \log{\left(\frac{a}{b}\right)}$.

3. Originally Posted by Prove It
Start by rewriting any term with a coefficient as a term with a power inside the logarithm (using the rule $p\log{a} = \log{(a^p)}$).

You should then be able to simplify the rest using the sum/difference rules $\log{a} + \log{b} = \log{(ab)}$ and $\displaystyle \log{a} - \log{b} = \log{\left(\frac{a}{b}\right)}$.
thank you so much!!