## Jamierox4ev3r one year ago Rewrite the following log expression using the law of logarithms. Your final answer should have no exponents and many logs.

1. Jamierox4ev3r

$$\huge\log \left( \frac{ x^{7} }{ \sqrt[3]{y^{2}z^{5}} } \right)$$

2. Jamierox4ev3r

I believe I have this one figured out, but I'm not sure, so I'll post my work and final answer

3. Jamierox4ev3r

$$\huge\log \left( \frac{ x^{7} }{ \sqrt[3]{y^{2}z^{5}} } \right)$$ $$\Large\log x^{7} - \log \sqrt[3]{y^{2}z^{5}}$$ $$\Large 7\log x - \log (y^{2}z^{5})^{\frac{1}{3}}$$ $$\Large 7\log x - \log (y^{\frac{2}{3}} z^{\frac{5}{3}})$$ $$\Large 7\log x - \log y^{\frac{2}{3}} + \log z^{\frac{5}{3}}$$ $$\Huge 7\log x - \frac{2}{3}\log y + \frac{5}{3}\log z$$ ^^ I believe that is my final answer. Someone please let me know if I'm right, or if I'm not, tell me where I went wrong. Thanks in advance.

4. anonymous

there's mistake in one sign.. check it..

5. Jamierox4ev3r

sign? you mean a discrepancy for whether something is positive or negative?

6. anonymous

yes

7. Jamierox4ev3r

Hmm...I think you may be talking about the 4/5 step, where I expanded the parentheses. but isn't it a rule that states this? log(MN) = logM + logN? Therefore, I don't see any error in my process there; at least, I don't think I see an error there.

8. anonymous

you stated right but check this -( log MN) = -log M -log N if you agree then check again that step

9. Jamierox4ev3r

Oh. So you believe that the negative sign distributes into the parentheses?

10. anonymous

I dont believe.. its maths :P

11. Jamierox4ev3r

lol whoops, wrong way of phrasing that. But I see what you mean, and thanks

12. anonymous

:)

13. Jamierox4ev3r

$$\Huge 7\log x - \frac{2}{3}\log y - \frac{5}{3}\log z$$ ^^ That should be the final answer then, if I'm not mistaken

14. anonymous

yep

15. Jamierox4ev3r

Awesome, I get it. Thank you ^_^

16. anonymous

nvm :)