Simplifying natural logarithmic equations

Question

Write as a single logarithm and simplify your answer.

I am totally unsure as to how far this can be simplified. Should I be factoring the quadratic and then using the product/quotient rules?

Any help would be amazing!

Answer 1

Use the facts that $$\ln M +\ln N =\ln MN$$ and $$\ln M -\ln N =\ln \frac{M}{N}$$ and $$a\ln M =\ln M ^a$$ Then your answer will come out to be $\ln\frac {(x^2+x+1)(x-1)^\frac {2}{3}}{x^2}$.

Hope this helps you.