## anonymous 3 years ago How to simplify 11/5 (ln2 - 1/2 (ln9) + 1/2 (ln6)?

1. anonymous

You have no variables, so can't you just solve it?

2. anonymous

i need to be in exact form

3. anonymous

Oh, right. Sorry, wasn't thinking.

4. anonymous

i dont know if i can just bring the 1/2 to the 9 , so it will be 3

5. anonymous

Well, $$1/2 \ln 9$$ is $$\ln 3$$, right?

6. anonymous

Yeah, because $$a \log x = \log x^a$$

7. anonymous

then will the final answer be (ln 2sqrt 6/ 3)?

8. anonymous

$\frac{11}{5} (\ln 2 - \ln 3 + \ln \sqrt{6}) = \frac{11}{5} (\ln \frac{2 \sqrt{6}}{3}) \text{ or } \ln (\frac{2 \sqrt{6}}{3})^{\frac{11}{5}}$ Is that math right?