# Simplifying natural logarithmic equations

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!

## 1 Answer

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.

• I know this isn't supposed to be used to say thank you, but I have to. I'm so grateful for your help! Seriously appreciate it. – edward Dec 6 '16 at 4:12
• @edward You're welcome. However, as you seem to be new here, I would like to inform you that if you like a particular answer, then you can upvote it by clicking the up arrow on the left of the answer and if it solves your problem completely and you understand it well, then you can accept it by clicking the tick (which appears green after clicking) on the left of the answer. – SchrodingersCat Dec 6 '16 at 4:17