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06-09-2016, 04:23 AM
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#1
solve
$Q1)2^{\frac{x+y}{3}}+2^{\frac{x+y}{6}}=6$
$x^{2}+5y^{2}=6xy$
$Q2)xy-x-y=5$
$2^{x-y}-(\frac{1}{2})^{x-y}=\frac{3}{2}$
$Q3)3^{x}5^{y}=75$
$ 3^{y}5^{x}=45$
$Q4)\log_{y}x+\log _{x}y=2$
$ x^{2}-y=20$
$Q5)5(\log_{y}x+\log _{x}y)=26$
$ xy=64$
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06-09-2016, 01:58 PM
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#2
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06-09-2016, 11:31 PM
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#3
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06-10-2016, 12:48 AM
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#4
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06-10-2016, 03:55 PM
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#5
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06-11-2016, 04:20 AM
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#6
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$Q5)5(\log_{y}x+\log _{x}y)=26$
$ xy=64$
$sol:$
$log_{y}x +\frac{1}{log_{y}x}=\frac{26}{5}$
$(log_{y}x)^{2}-\frac{26}{5}log_{y}x +1=0$
$(log_{y}x-5)(log_{y}x-\frac{1}{5})=0$
$either y^{5}=x\rightarrow y^{6}=64\rightarrow y=2,x=32$
$or y^{\frac{1}{5}}=x\rightarrow x^{5}=y\rightarrow x^{6}=64\rightarrow x=2,y=32$
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06-11-2016, 04:41 AM
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#7
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$Q6)log_{2}(x+y)+log_{3}(x-y)=1$
$ x^{2}-y^{2}=2$
$Q7)y=1+log_{4}x$
$x^{y}=4^{6}$
$Q8)y^{\frac{1}{x}}=2$
$y^{x}=16$
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06-11-2016, 02:49 PM
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#8
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06-11-2016, 04:23 PM
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#9
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06-12-2016, 01:21 AM
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#10
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$Q9)xy=16$
$ x^{log_{2}y}=8$
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06-12-2016, 05:05 PM
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#11
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06-13-2016, 12:23 AM
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#12
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$Q10)x^{\frac{-1}{2}} + y^{\frac{-1}{2}}=6$
$log_{4}x+log_{4}y=-3$
$Q11)\sqrt{\frac{x}{y}}-\sqrt{\frac{y}{x}}=\frac{3}{2}$
$xy+x+y=9$
$Q12)log_{y}x=2$
$x^{logy}=100$
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