Question

Equação exponencial:
$4^{x+2} - 3.2^{x+3} = 160$

Answer 1

Oi Senhorita.

$4^{ x+2 }-3*2^{ x+3 }=160\\ (2^{ x })^{ 2 }*2^{ 2 }-3*2^{ x }*2^{ 3 }=160\\ (2^{ x })^{ 2 }*4-24*2^{ x }=160\\ 2^{ x }=y\\ \\ 4y^{ 2 }-24y=160\quad (:4)\\ y^{ 2 }-6y-40=0\\ \\ (y+10)(y-4)\\ \\ y+10=0\\ y=-10\\ \\ y-4=0\\ y=4\\ \\ 2^{ x }=4\\ 2^{ x }=2^{ 2 }\\ x=2$