Logarithm question

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\(\large \color{black}{\begin{align}&\text{express }\ \log \dfrac{a^{2/3}}{b^{5}\sqrt{c}} \hspace{.33em}\\~\\ & a.)\ \dfrac{3}{2}\log a+5\log b-2\log c \hspace{.33em}\\~\\ & b.)\ \dfrac{2}{3}\log a-5\log b-2\log c \hspace{.33em}\\~\\ & c.)\ \dfrac{2}{3}\log a-5\log b+2\log c \hspace{.33em}\\~\\ & d.)\ \dfrac{3}{2}\log a+5\log b-2\log c \hspace{.33em}\\~\\ \end{align}}\)
we need the log rules for this one... so all three of them are being used.
|dw:1437810148932:dw|

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Other answers:

\[\log a^\frac{ 2 }{ 3 } -\log b^5-\log c^\frac{ 1 }{ 2 }\]
is it option c.) ?
here's a problem .. those choices have 2 for c instead of a 1/2
... otherwise the a and b portions are correct but one rule is needed ... exponent rule
Yeah it should be 1/2 though since c^1/2
except 2 is it option c.)
|dw:1437810300989:dw| < - this rule needs to be used after doing the other 2 log rules.
i mean is option c.) correct except the rule on 2 instead of 1/2
|dw:1437810360573:dw|
option c.) -.-
wait a sec.. by elevator rule we should have a negative exponent on top..
|dw:1437810460826:dw| <-- example
my head hurts
|dw:1437810507720:dw|
|dw:1437810508756:dw|
thanks @Deeezzzz
|dw:1437810548559:dw|
correct
is it option b.)
yes it is B
cookie monster almost tricked me into using the elevator rule wrong -___- BAD COOKIE MONSTER! NO COOKIES FOR YOU! YOU GET GRANOLA BARS INSTEAD!
my head hurts
and the elevator rule *gives granola bar*
what is gronola bar ?
has flax seeds in em.. and raisins.
LOL
is it better than cookies
-_- I think cookie man is right... with the exception of that 2 for c (not sure how they got that) \[ \large \log \dfrac{a^{2/3}}{b^{5}\sqrt{c}} \] \[ \large \log \dfrac{a^{2/3}}{b^{5}c^{\frac{1}{2}}} \] \[\large \log a^{\frac{2}{3}}- \log b^5-logc^{-\frac{1}{2}}\] \[\frac{2}{3}\log a-5\log b-(-\frac{1}{2}) \log c\] \[\frac{2}{3}\log a-5\log b+\frac{1}{2} \log c \]
errr awkward... no refunds ^^
*head bang
guys cookie man is right.. it was distribution towards the end that made the sign change x(
http://www.wolframalpha.com/input/?i=simplify+%5Clog+%5Cdfrac%7Ba%5E%7B2%2F3%7D%7D%7Bb%5E%7B5%7D%5Csqrt%7Bc%7D%7D
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 -
oh it's a combination... of the minus from the log rule and the negative exponent... x(
|dw:1437811756674:dw|
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.
|dw:1437812129408:dw|
oh that's what happened I got something mixed up doh! it is - 1/2 log c at the end ^_^
Lol

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