Question

5º. O conjunto solução da equação exponencial 2^(x+3)-2^(x+1)-2^x=5 é:
Alternativa 1: S={0;1}
Alternativa 2: S={1}
Alternativa 3: S={0}
Alternativa 4: S={2}
Alternativa 5: S={1;2}

Answer 1

Boa tarde Mota!

Solução!

$2^{x+3}-2^{x+1}-2^{x}=5\\\\\\ 2^{x}.2^{3} -2^{x}.2^{1}-2^{x}=5\\\\\\\ Colocando ~~em ~~evidencia ~~2^{x}\\\\\\ 2^{x}(2^{3} -2^{1} -1)=5\\\\\\ 2^{x}(8-2 -1)=5\\\\\\ 2^{x}(8-3)=5\\\\\\ 2^{x}(5)=5\\\\\\ 2^{x}= \dfrac{5}{5} \\\\\\ 2^{x}= 1$

Lembrando que todo numero elevado a zero é igual a 1.

$2^{0}=1\\\\\\ 2^{x}=2^{0} \\\\\ 2^{x}=1 \\\\\\\\\\\\\ \boxed{Resposta:2^{x+3}-2^{x+1}-2^{x}=5 ~~S=\{0\}~~ \boxed{ Alternativa~~3}}$