## mathmath333 one year ago Logarithm question

1. mathmath333

\large \color{black}{\begin{align}&\text{express }\ \log \dfrac{a^{2/3}}{b^{5}\sqrt{c}} \hspace{.33em}\\~\\ & a.)\ \dfrac{3}{2}\log a+5\log b-2\log c \hspace{.33em}\\~\\ & b.)\ \dfrac{2}{3}\log a-5\log b-2\log c \hspace{.33em}\\~\\ & c.)\ \dfrac{2}{3}\log a-5\log b+2\log c \hspace{.33em}\\~\\ & d.)\ \dfrac{3}{2}\log a+5\log b-2\log c \hspace{.33em}\\~\\ \end{align}}

2. UsukiDoll

we need the log rules for this one... so all three of them are being used.

3. UsukiDoll

|dw:1437810148932:dw|

4. anonymous

$\log a^\frac{ 2 }{ 3 } -\log b^5-\log c^\frac{ 1 }{ 2 }$

5. mathmath333

is it option c.) ?

6. UsukiDoll

here's a problem .. those choices have 2 for c instead of a 1/2

7. UsukiDoll

... otherwise the a and b portions are correct but one rule is needed ... exponent rule

8. anonymous

Yeah it should be 1/2 though since c^1/2

9. mathmath333

except 2 is it option c.)

10. UsukiDoll

|dw:1437810300989:dw| < - this rule needs to be used after doing the other 2 log rules.

11. mathmath333

i mean is option c.) correct except the rule on 2 instead of 1/2

12. UsukiDoll

|dw:1437810360573:dw|

13. mathmath333

option c.) -.-

14. UsukiDoll

wait a sec.. by elevator rule we should have a negative exponent on top..

15. UsukiDoll

|dw:1437810460826:dw| <-- example

16. mathmath333

17. UsukiDoll

|dw:1437810507720:dw|

18. anonymous

|dw:1437810508756:dw|

19. UsukiDoll

thanks @Deeezzzz

20. UsukiDoll

|dw:1437810548559:dw|

21. anonymous

correct

22. mathmath333

is it option b.)

23. anonymous

yes it is B

24. UsukiDoll

25. mathmath333

26. UsukiDoll

and the elevator rule *gives granola bar*

27. mathmath333

what is gronola bar ?

28. UsukiDoll

has flax seeds in em.. and raisins.

29. sweetburger

LOL

30. mathmath333

31. UsukiDoll

-_- I think cookie man is right... with the exception of that 2 for c (not sure how they got that) $\large \log \dfrac{a^{2/3}}{b^{5}\sqrt{c}}$ $\large \log \dfrac{a^{2/3}}{b^{5}c^{\frac{1}{2}}}$ $\large \log a^{\frac{2}{3}}- \log b^5-logc^{-\frac{1}{2}}$ $\frac{2}{3}\log a-5\log b-(-\frac{1}{2}) \log c$ $\frac{2}{3}\log a-5\log b+\frac{1}{2} \log c$

32. UsukiDoll

errr awkward... no refunds ^^

33. mathmath333

34. UsukiDoll

guys cookie man is right.. it was distribution towards the end that made the sign change x(

35. mathmath333
36. UsukiDoll

oh ok I guess it was the - sign... it's a bit confusing because at first when I was doing the problem it will come up as a minus... but we are also dealing with a negative exponent too ... unless that negative from the exponent and the minus sign from the log rule... is just one -

37. UsukiDoll

oh it's a combination... of the minus from the log rule and the negative exponent... x(

38. UsukiDoll

|dw:1437811756674:dw|

39. UsukiDoll

I'm confused for the last part... x.x any clarification? or a memory refresher... it's like the subtraction rule and exponent rule is being used at the same time for that c.

40. anonymous

|dw:1437812129408:dw|

41. UsukiDoll

oh that's what happened I got something mixed up doh! it is - 1/2 log c at the end ^_^

42. anonymous

Lol