## santw 3 years ago How do i simplify?

1. santw

$5x=\frac{ \log_{}4 }{ \log_{}3 }$

2. santw

i need to solve for x.

3. EpikRebel

Wow this basically reminded me to refresh up on my Algebra 2.

4. santw

i just don't know how i would divide 5 by log4/log3.

5. SheldonEinstein

This involves the properties of logarithm. @santw loga/logb = ?

6. SheldonEinstein

Wait!

7. santw

i tried that. my solutions manual gives a diff answer. @SheldonEinstein

8. SheldonEinstein

$\large{\frac{log_b m}{log_b n} = log_b {m-n}}$

9. SheldonEinstein

10. santw

i'm trying to refrain from looking at the answers. but it shows me log4/5 log3? i'm lost.

11. santw

0.2524 @SheldonEinstein

12. zepdrix

So they just divided both sides by 5..?

13. SheldonEinstein

Very near lol

14. santw

yes. @zepdrix i think my question is. how do you divide a fraction by a fraction?

15. SheldonEinstein

log(4)/log(3) /5/1 = $\large{\frac{log(4)}{log(3)}\times \frac{1}{5}}$

16. SheldonEinstein

$\large{\cfrac{\frac{a}{b}}{\frac{c}{d}} = \frac{a}{b} \times \frac{d}{c}}$

17. SheldonEinstein

|dw:1351139061407:dw|

18. SheldonEinstein

So this is how we divide fraction by fraction @santw got it?

19. santw

got it! thanks! @SheldonEinstein

20. SheldonEinstein

You're welcome and also, good work @zepdrix

21. zepdrix

lol :d Yayyyy for hello kitty! \:D/

22. SheldonEinstein

:D