Question

respondam pra mim por favor!!!

Answer 1

Faça a substituição:  $2^x=y$

$2y+\frac{y}{4}=\frac{9}{2}\\ \\ Multiplique \ por \ 4:\\ \\ 8y+y=18\\ \\ 9y=18\\ \\ y=2\\ \\ Logo: 2^x=2 \Rightarrow 2^x=2^1\Rightarrow x=1$

Answer 2

$2^{x}\cdot2+\dfrac{2^{x}}{2^2}=\dfrac{9}{2}~~\Rightarrow~~2^{x}\cdot2+2^{x}\cdot\dfrac{1}{4}=\dfrac{9}{2}$

$2^{x}\cdot\left(2+\dfrac{1}{4}\right)=\dfrac{9}{2}~~\Rightarrow~~2^{x}\cdot\dfrac{9}{4}=\dfrac{9}{2}$

$2^{x}=\dfrac{\dfrac{9}{2}}{\dfrac{9}{4}}~~\Rightarrow~~2^{x}=\dfrac{4}{2}$

$2^{x}=2~~\Rightarrow~~2^{x}=2^{1}~~\Rightarrow~~\boxed{x=1}$.