Question

РЕШИТЕ СИСТЕМЫ УРАВНЕНИЙ!!!!!ПОЖАЛУЙСТА!!!

Answer 1

а) $left { {{log_{4}x-log_{4}y=1} atop {x-3y=16}} right.$

$left { {{log_{4}x-log_{4}y=1} atop {x=16+3y}} right.$

$left { {{log_{4}(16+3y)-log_{4}y=1} atop {x=16+3y}} right.$

$left { {{log_{4}( frac{16+3y}{y})=log_{4}4} atop {x=16+3y}} right.$

$left { {{frac{16+3y}{y}=4} atop {x=16+3y}} right.$

$left { {{16+3y=4y} atop {x=16+3y}} right.$

$left { {{y=16} atop {x=16+3y}} right.$

$left { {{y=16} atop {x=16+3*16=64}} right.$

ОДЗ: x>0, y>0

Ответ: (64;16)

б) $left { {{log_{2}(x-y)=1} atop {2^{x}*3^{y+1}=72}} right.$

$left { {{x-y=2} atop {2^{x}*3^{y}*3}=72}} right.$

$left { {{x=2+y} atop {2^{x}*3^{y}*3}=72}} right.$

$left { {{x=2+y} atop {2^{2+y}*3^{y}*3}=72}} right.$

$left { {{x=2+y} atop {4*2^{y}*3^{y}*3}=72}} right.$

$left { {{x=2+y} atop {2^{y}*3^{y}=6}} right.$

$left { {{x=2+y} atop {6^{y}=6}} right.$

$left { {{x=2+y} atop {y=1}} right.$

$left { {{x=2+1=3} atop {y=1}} right.$

ОДЗ: x-y>0

Ответ: (3;1)