Question

Equações Exponenciais:
1) Resolva os sistemas abaixo:

a) $2^{2+y} = 2^{-2} 4^{2x} : 4^{-y} = 1$

b) $3^{x+y}=3^{-2}  5^{2x} : 5^{y}=1$

Answer 1

a)
$1)2^{2+y}=2^{-2} \\\\ 2+y=-2 \\\\ y=-2-2 \\\\ y=-4$


$2)4^{2x}:4^{-y}=1 \\\\ 4^{2x-(-y)}=1\\\\4^{2x+y}=4^0 \\ \\ 2x+(-4)=0 \\ \\ 2x-4=0 \\ \\ 2x=4 \\ \\ x=4:2 \\ \\ x=2$





b)
$1)3^{x+y}=3^{-2} \\ \\x+y=-2 \\\\ y=x-2$


$2)5^{2x}:5^y=1 \\ \\ 5^{2x-y}=1 \\ \\ 5^{2x-y}=5^0 \\ \\ 2x-y=0 \\ \\ 2x=y \\ \\ 2x=(x-2) \\ \\ 2x=x-2 \\ \\ 2x-x=-2\\\\x=-2$


$1)y=x-2 \\ \\ y=(-2)-2 \\ \\ y=-2-2 \\ \\ y=-4$