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}
Respostas
respondido por:
3
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\\\\\\](https://tex.z-dn.net/?f=2%5E%7Bx%2B3%7D-2%5E%7Bx%2B1%7D-2%5E%7Bx%7D%3D5%5C%5C%5C%5C%5C%5C%0A2%5E%7Bx%7D.2%5E%7B3%7D+-2%5E%7Bx%7D.2%5E%7B1%7D-2%5E%7Bx%7D%3D5%5C%5C%5C%5C%5C%5C%5C%0AColocando+%7E%7Eem+%7E%7Eevidencia+%7E%7E2%5E%7Bx%7D%5C%5C%5C%5C%5C%5C%0A+2%5E%7Bx%7D%282%5E%7B3%7D+-2%5E%7B1%7D++-1%29%3D5%5C%5C%5C%5C%5C%5C%0A++2%5E%7Bx%7D%288-2++-1%29%3D5%5C%5C%5C%5C%5C%5C%0A++2%5E%7Bx%7D%288-3%29%3D5%5C%5C%5C%5C%5C%5C%0A2%5E%7Bx%7D%285%29%3D5%5C%5C%5C%5C%5C%5C%0A2%5E%7Bx%7D%3D+%5Cdfrac%7B5%7D%7B5%7D+%5C%5C%5C%5C%5C%5C%0A2%5E%7Bx%7D%3D+1%5C%5C%5C%5C%5C%5C "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}}](https://tex.z-dn.net/?f=2%5E%7B0%7D%3D1%5C%5C%5C%5C%5C%5C%0A2%5E%7Bx%7D%3D2%5E%7B0%7D+%5C%5C%5C%5C%5C%0A2%5E%7Bx%7D%3D1+%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%0A%5Cboxed%7BResposta%3A2%5E%7Bx%2B3%7D-2%5E%7Bx%2B1%7D-2%5E%7Bx%7D%3D5+%7E%7ES%3D%5C%7B0%5C%7D%7E%7E+%5Cboxed%7B+Alternativa%7E%7E3%7D%7D "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}}")
Solução!
Lembrando que todo numero elevado a zero é igual a 1.
mota270615:
gostei da resposta me ajudou muito
Que bom!
Perguntas similares
7 anos atrás
9 anos atrás
9 anos atrás
9 anos atrás
9 anos atrás