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    solve these two equations simultaneously: 4log_9 x + 4log_xy=9 and 6log_3 x + 6log_2_7 y = 7 and I worked a bit on them to get log_3 y^6 x^1^8 =21 and log_3 x^4 y^8=18...not sure what to do next... how can I eliminate log_3??
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    (Original post by JacobAlevels)
    solve these two equations simultaneously: 4log_9 x + 4log_xy=9 and 6log_3 x + 6log_2_7 y = 7 and I worked a bit on them to get log_3 y^6 x^1^8 =21 and log_3 x^4 y^8=18...not sure what to do next... how can I eliminate log_3??
    I haven't checked your working but note that

    y^6x^{18} = (y^2x^6)^3

    and

    x^4y^8 = (x^2y^4)^2

    so you can take some powers outside the log using the standard log rules.
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    (Original post by JacobAlevels)
    solve these two equations simultaneously: 4log_9 x + 4log_xy=9 and 6log_3 x + 6log_2_7 y = 7 and I worked a bit on them to get log_3 y^6 x^1^8 =21 and log_3 x^4 y^8=18...not sure what to do next... how can I eliminate log_3??
    If I were you I would rewrite all logarithm to base 3 and substitute log_3 x = a and log_3 y=b

    \displaystyle 4log_9 x + 4log_xy=9 \rightarrow 4\cdot \frac{log_3 x}{log_3 9} +4\cdot \frac{log_3 y}{log_3 x}=9 \rightarrow 2 a +4\frac{b}{a}=9

    and

    \displaystyle 6log_3 x+6log_{27} y=7 \rightarrow 6log_3 x+6\frac{log_3 y}{log_3 27}=7 \rightarrow 6a+2b=7

    Solve them simultaneously, then from a and b you will get x and y.
 
 
 
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