anonymous
  • anonymous
Simplify the expression attached and write it as a single logarithm.. ***still confused on this topic... pls help? :)
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
anonymous
  • anonymous
answer choices A,B,C,D from top to bottom :)
tkhunny
  • tkhunny
Move all the exponents up: \((x+4)^{-3}\) \((x-7)^{2}\) \((x-2)^{5}\) \((x^{2})^{-1}\) Notice how I deliberately left everything outside as ADDITION. This allows us just to bring everything inside without concern for numerator or denominator. We can figure all that out later.

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anonymous
  • anonymous
im confused.. so how can i apply that with my expression?
tkhunny
  • tkhunny
Confused with what? \(-3\log(x+4) = \log\left[\left(x+4\right)^{-3}\right]\) Correct?
anonymous
  • anonymous
im not quite sure what we are working on now.. I'm like uber confused.. are we doing my problem? or an example? :/ sorry I'm a bit confused :(
tkhunny
  • tkhunny
Your problem statement begins \(-3\log(x+4)\), doesn't it? Or am I looking at some other picture?
anonymous
  • anonymous
yup iy does :) so i get log[(x+4)^−3] from that part?
tkhunny
  • tkhunny
Very good. Now the (x-7) part?
anonymous
  • anonymous
2log(x-7) = log(x-7)^2 ??
tkhunny
  • tkhunny
Good, now the x-2...
anonymous
  • anonymous
5log(x-2)=log(x-2)^5 ??
tkhunny
  • tkhunny
One more. You're on a roll!
anonymous
  • anonymous
lol thanks haha :P but i don't get this one... it looks different.. :/ -logx^2...
anonymous
  • anonymous
but heres my take on it.. log(x^2)^-1 ??
tkhunny
  • tkhunny
Take the negative (-1) inside, just like the other coefficients ==> exponents.
anonymous
  • anonymous
was what i got right?? or no?
anonymous
  • anonymous
or is it log(x)^-2 ?
tkhunny
  • tkhunny
There it is. They are now all connected by addition. Use this guy and bring them all together. log(a) + log(b) = log(a*b)
anonymous
  • anonymous
sorry my computer crashed... one sec :/
anonymous
  • anonymous
log[(x+4)^−3]+ log(x-2)^5+log(x-7)^2 + log(x)^-2=answer B right? :)
jim_thompson5910
  • jim_thompson5910
use the rule described above to go from log[(x+4)^−3]+ log(x-2)^5+log(x-7)^2 + log(x)^-2 to log[ (x+4)^−3*(x-2)^5*(x-7)^2*(x)^-2 ]
anonymous
  • anonymous
kk I'm seeing that :) but how can i simplify it even further?
jim_thompson5910
  • jim_thompson5910
(x+4)^−3 is really 1/[ (x+4)^3 ]
jim_thompson5910
  • jim_thompson5910
same idea applies to (x)^-2
anonymous
  • anonymous
ok so i get 1/x^-2 ?
jim_thompson5910
  • jim_thompson5910
yep
jim_thompson5910
  • jim_thompson5910
so put that all together
anonymous
  • anonymous
so i get answer C right?? :)
anonymous
  • anonymous
sorry i meant answer D :) is it answer D then? :)
anonymous
  • anonymous
@jim_thompson5910 :)
jim_thompson5910
  • jim_thompson5910
yes it is D
anonymous
  • anonymous
kk great!!! thx :)

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