iheartfood
question attached inside!! :)



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iheartfood
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part 1 of question :)

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

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

jim_thompson5910
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all logs in this particular problem are base b

iheartfood
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kk so that means? haha :P

jim_thompson5910
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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?

jim_thompson5910
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no i said that as a disclaimer to what I was about to write

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

iheartfood
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or do i do substitution or sometihng?

jim_thompson5910
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you can pull the exponents down

jim_thompson5910
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using one of the rules given on that purplemath site

iheartfood
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oh no!! i lost the link :(

iheartfood
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can u pls resend it to me? :)


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

jim_thompson5910
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you use the rule that log(x^y) = y*log(x)

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

jim_thompson5910
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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

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

jim_thompson5910
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log(A) = 5, so replace log(A) with 5
do the same with the other logs

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


jim_thompson5910
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you mixed up C and D though and you're missing your coefficients

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

jim_thompson5910
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look at the givens again

iheartfood
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the givens?

iheartfood
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what are the givens?? from the original question?

jim_thompson5910
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yeah, log(A) = ..., log(C) = ..., etc

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

jim_thompson5910
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ok, now add on the coefficients

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

jim_thompson5910
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oh wait, idk why i said that was right, I'm misreading lol

jim_thompson5910
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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) ) = ???

jim_thompson5910
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log(A) = 5
NOT log(5)

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

jim_thompson5910
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no sry, but i put up the right way to do it

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

jim_thompson5910
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hmm no

jim_thompson5910
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that looks off

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

jim_thompson5910
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\[\Large \log_{b}\left(\frac{A^5C^2}{D^6}\right) = \log_{b}\left(A^5C^2\right)  \log_{b}\left(D^6\right)\]
\[\Large \log_{b}\left(\frac{A^5C^2}{D^6}\right) = \log_{b}\left(A^5\right) + \log_{b}\left(C^2\right)  \log_{b}\left(D^6\right)\]
\[\Large \log_{b}\left(\frac{A^5C^2}{D^6}\right) = 5\log_{b}\left(A\right) + 2\log_{b}\left(C\right)  6\log_{b}\left(D\right)\]
\[\Large \log_{b}\left(\frac{A^5C^2}{D^6}\right) = 5(5) + 2(7)  6(2)\]
\[\Large \log_{b}\left(\frac{A^5C^2}{D^6}\right) = ???\]

iheartfood
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27??

iheartfood
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so my answer is B. 27 ???


iheartfood
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thank youuu :)