Question

Resolva a equação exponencial:
$2 ^{2x+1} + 3.2^{x+1} = 8$

Answer 1

Oi Senhorita.

$2^{ 2x+1 }+3*2^{ x+1 }=8\\ 2^{ 2x }*2+3*2^{ x }*2=8\\ (2^{ x })^{ 2 }*2+2^{ x }*6=8\\ 2^{ x }=y\\ \\ 2y^{ 2 }+6y=8\quad (:2)\\ y^{ 2 }+3y-4=0\\ \\ (y+4)(y-1)\\ \\ y+4=0\\ y=-4\\ \\ y-1=0\\ y=1\\ \\ 2^{ x }=1\\ 2^{ x }=2^{ 0 }\\ x=0$