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## iheartfood 3 years ago question attached inside!! :)

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1. iheartfood

part 1 of question :)

2. iheartfood

part 2 (last part!) of the question :) they are connected, but just one problem :)

3. iheartfood

A. -1 B. 27 C. 29 D. There isn't enough information to answer the question. idk :/

4. jim_thompson5910

all logs in this particular problem are base b

5. iheartfood

kk so that means? haha :P

6. jim_thompson5910

log( (A^5C^2)/(D^6) ) = log(A^5C^2) - log(D^6) log( (A^5C^2)/(D^6) ) = log(A^5) + log(C^2) - log(D^6) What's next?

7. jim_thompson5910

no i said that as a disclaimer to what I was about to write

8. iheartfood

oh okay haha :P so do i simplify that more? or is that the most simplified it can get?

9. iheartfood

or do i do substitution or sometihng?

10. jim_thompson5910

you can pull the exponents down

11. jim_thompson5910

using one of the rules given on that purplemath site

12. iheartfood

oh no!! i lost the link :(

13. iheartfood

can u pls resend it to me? :)

14. jim_thompson5910
15. iheartfood

okay so which one do i use?? I'm confused :(

16. jim_thompson5910

you use the rule that log(x^y) = y*log(x)

17. iheartfood

so I'm trying to see what to put in here, but I'm stuck... idk :(

18. jim_thompson5910

log( (A^5C^2)/(D^6) ) = log(A^5C^2) - log(D^6) log( (A^5C^2)/(D^6) ) = log(A^5) + log(C^2) - log(D^6) log( (A^5C^2)/(D^6) ) = 5*log(A) + 2*log(C) - 6*log(D) Then do the proper substitutions

19. iheartfood

ohhh i see what u did now! but how do i do proper substitutions??

20. jim_thompson5910

log(A) = 5, so replace log(A) with 5 do the same with the other logs

21. iheartfood

so i get log(5)+log(2)-log(6) ??

22. jim_thompson5910

close

23. jim_thompson5910

you mixed up C and D though and you're missing your coefficients

24. iheartfood

okay then, idk then :( iheartfood=a confused person atm :/

25. jim_thompson5910

look at the givens again

26. iheartfood

the givens?

27. iheartfood

what are the givens?? from the original question?

28. jim_thompson5910

yeah, log(A) = ..., log(C) = ..., etc

29. iheartfood

okay so i get this? log(5)+log(7)-log(2) ??

30. jim_thompson5910

ok, now add on the coefficients

31. iheartfood

what coefficients?? like the results when i enter it in the calc??

32. jim_thompson5910

oh wait, idk why i said that was right, I'm misreading lol

33. jim_thompson5910

log( (A^5C^2)/(D^6) ) = log(A^5C^2) - log(D^6) log( (A^5C^2)/(D^6) ) = log(A^5) + log(C^2) - log(D^6) log( (A^5C^2)/(D^6) ) = 5*log(A) + 2*log(C) - 6*log(D) log( (A^5C^2)/(D^6) ) = 5*5 + 2*7 - 6*2 log( (A^5C^2)/(D^6) ) = ???

34. jim_thompson5910

log(A) = 5 NOT log(5)

35. iheartfood

wiat so what do i have now then?? I'm confused now lol

36. jim_thompson5910

no sry, but i put up the right way to do it

37. iheartfood

so i have this so far?|dw:1353219981709:dw|??just making sure... idk if thats how I'm supposed to draw it?

38. jim_thompson5910

hmm no

39. jim_thompson5910

that looks off

40. iheartfood

can u pls draw it for me?? idk how to comprehend that well when its like in font/text format :/

41. jim_thompson5910

$\Large \log_{b}\left(\frac{A^5C^2}{D^6}\right) = \log_{b}\left(A^5C^2\right) - \log_{b}\left(D^6\right)$ $\Large \log_{b}\left(\frac{A^5C^2}{D^6}\right) = \log_{b}\left(A^5\right) + \log_{b}\left(C^2\right) - \log_{b}\left(D^6\right)$ $\Large \log_{b}\left(\frac{A^5C^2}{D^6}\right) = 5\log_{b}\left(A\right) + 2\log_{b}\left(C\right) - 6\log_{b}\left(D\right)$ $\Large \log_{b}\left(\frac{A^5C^2}{D^6}\right) = 5(5) + 2(7) - 6(2)$ $\Large \log_{b}\left(\frac{A^5C^2}{D^6}\right) = ???$

42. iheartfood

27??

43. iheartfood

so my answer is B. 27 ???

44. jim_thompson5910

yes

45. iheartfood

thank youuu :)

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