решите систему уравнений 2^x*3^y=12 ...

July 2022 1 0 Report

решите систему уравнений 2^x*3^y=12

3^x*2^y=18

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RomeMin

Verified answer

$\left \{ {{2^{x}*3^{y}=12} \atop {3^{x}*2^{y}=18}} \right. \\ \left \{ {{2^{x}*3^{y}=2^{2}*3} \atop {3^{x}*2^{y}=3^{2}*2}} \right. \\ \left \{ {{2^{x-2}*3^{y-1}=1} \atop {3^{x-2}*2^{y-1}=1}} \right. \\ \left \{ {{2^{x-y-1}*3^{y-x+1}=1} \atop {2^{x+y-3}*3^{y-x-3}=1} \right. \\ \left \{ {{(2/3)^{x-y-1}=1} \atop {(2/3)^{x+y-3}=1}} \right. \\ \left \{ {{x-y=1} \atop {x+y=3}} \right. \\ \left \{ {{x=y+1} \atop {2y=2}} \right. \\ \left \{ {{y=1} \atop {x=2}} \right.$

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