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  1. Top | #1

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    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$
    ; 06-11-2016 04:19 AM

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  3. Top | #2

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  11. Top | #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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  13. Top | #7

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    :

    $Q6)log_{2}(x+y)+log_{3}(x-y)=1$

    $ x^{2}-y^{2}=2$


    $Q7)y=1+log_{4}x$

    $x^{y}=4^{6}$


    $Q8)y^{\frac{1}{x}}=2$

    $y^{x}=16$
    ; 06-11-2016 04:43 AM

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    ; 06-12-2016 01:09 AM

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  17. Top | #9

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  19. Top | #10

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    $Q9)xy=16$

    $ x^{log_{2}y}=8$

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  21. Top | #11

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  23. Top | #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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