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Ответ:

Объяснение:

[tex]\displaystyle\\\left \{ {{xy=40} \atop {x^{\lg(y)}}=4} \right. ~~~~~~~\boxed{ODZ:y > 0}\\\\\\\left \{ {{y=\dfrac{40}{x} } \atop {x^{\lg(\frac{40}{x}) }=4} \right. \\\\\bf\\lgx^{lg(\frac{40}{x})} =lg4\\\\lg\bigg(\frac{40}{x} \bigg)*lgx=lg4\\\\(lg4+lg10-lgx)*lgx=lg4\\\\lg^2x-lgx-lgx*lg4+lg4=0\\\\lgx(lgx-1)-lg4(lgx-1)=0\\\\(lgx-1)(lgx-lg4)=0\\\\1)lgx=1;x=10;y=4\\\\2)lgx=lg4;x=4;y=10\\\\otvet:(4;10)~(10;4)[/tex]

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[tex]\log_ab^n=n*\log_ab\\\\\log_a(b*c)=\log_ab+\log_ac[/tex]