King
  • King
Its a log question so i shall give it in the reply......
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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King
  • King
\[\log_{3} (\log_{2} x) + \log_{1/3} (\log_{2} y)=1.\] Find x,y if given \[xy ^{2}=4\]
anonymous
  • anonymous
alright what have you tried ?
King
  • King
um i took log base 1/3 as log base 3^-1 and that will be \[-\log_{3} \]

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anonymous
  • anonymous
log3(log2,x) + log1/3(log2,y) =1 log3(log2,x) - log3(log2,y) =1 log3(log2,x/log2,y) =1 log3(x/y) =1 x/y=3
anonymous
  • anonymous
replace 1 with log base 3 of 3 then: \[\log_{3}(\log_{2}x) - \log_{3}(\log_{2}y) = \log_{3}3 \] then:\[\log_{2}x / \log_{2}y = 3\] \[\log_{y}x = 3 \] y^3 = x so y is 4^0.2 x = 4^0.6
King
  • King
can u please xplain how u got the 3rd equation?
anonymous
  • anonymous
log a - log b = log(a/b)
anonymous
  • anonymous
@King:From the first equation I got $\frac{x}{y} = 3$ can you do the rest ?
King
  • King
no log x base y
King
  • King
xplain
anonymous
  • anonymous
oh ok. log a / log b = log a base b
anonymous
  • anonymous
if they both have the same base. that is the rule
King
  • King
FFM what have u written?$\frac{x}{y} = 3$
King
  • King
oh ok
King
  • King
so ok how to find x,y
anonymous
  • anonymous
read the rest. y^3 is x. and just plug that into your other equation
anonymous
  • anonymous
yes king
anonymous
  • anonymous
king its just substitution in the rest parts ..
anonymous
  • anonymous
xy^2 becomes y^5 so y^5 =4 so y = 4^0.2 and x = y^3 = 4^0.6
King
  • King
ok...thnx guys can u solve 1 more question....shall i post it?
anonymous
  • anonymous
go ahead

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