Question

Se 2^x4^y=32 e 3^x/9^y=3, então 5^x/125^y=

Answer 1

$2^x.4^y=32 \\ 2^x\times2^{2y}=2^5 \\ x+2y=5~~(I) \\ \\ \frac{3^x}{9^y} =3 \\ \\ 3^x\div3^{2y}=3 \\ x-2y=1~~(II) \\ \\ \left \{ {{x+2y=5} \atop {x-2y=1}} \right.$

sistema pela adição, cancela 2y (2y-2y=0) e soma

$x+x=5+1 \\ 2x=6 \\ x=6\div2 \\\fbox{ x=3 } \\ \\ substituir~~x~~em \\ \\ x+2y=5 \\ 3+2y=5 \\ 2y=5-3 \\ y=5-3 \\ 2y=2 \\ y=2\div2 \\\fbox{ y=1 }$~

$Calculando \\ \\ \frac{5^x}{125^y} =5^x\div5^{3y}=5^3\div5^{3(1)}=5^5\div5^3=5^{5-5}=5^0=\fbox{ 1 }$