Determine o conjunto solução da equação 2^x+3 + 2^x = 144
ElenBru:
Só, o que significa esse ^?
elevado
tipo... 2 elevado a x+3
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Boa tarde Thalia!
Solução!
![2^{x+3} +2^{x}=144\\\\\\\
2^{x}.2^{3}+2^{x}=144\\\\\\
2^{x}(2^{3}+1)=144\\\\\\\
2^{x}(8+1)=144\\\\\\
2^{x}(9)=144](https://tex.z-dn.net/?f=2%5E%7Bx%2B3%7D+%2B2%5E%7Bx%7D%3D144%5C%5C%5C%5C%5C%5C%5C%0A2%5E%7Bx%7D.2%5E%7B3%7D%2B2%5E%7Bx%7D%3D144%5C%5C%5C%5C%5C%5C%0A2%5E%7Bx%7D%282%5E%7B3%7D%2B1%29%3D144%5C%5C%5C%5C%5C%5C%5C%0A2%5E%7Bx%7D%288%2B1%29%3D144%5C%5C%5C%5C%5C%5C%0A2%5E%7Bx%7D%289%29%3D144++++++++ "2^{x+3} +2^{x}=144\\\\\\\
2^{x}.2^{3}+2^{x}=144\\\\\\
2^{x}(2^{3}+1)=144\\\\\\\
2^{x}(8+1)=144\\\\\\
2^{x}(9)=144")
![2^{x}= \frac{144}{9}\\\\\\
2^{x}=16\\\\\
2^{x}=2^{4}\\\\\\\
x=4\\\\\\\\\\\
\boxed{Resposta:~~S=\{4\}}](https://tex.z-dn.net/?f=2%5E%7Bx%7D%3D+%5Cfrac%7B144%7D%7B9%7D%5C%5C%5C%5C%5C%5C%0A2%5E%7Bx%7D%3D16%5C%5C%5C%5C%5C%0A2%5E%7Bx%7D%3D2%5E%7B4%7D%5C%5C%5C%5C%5C%5C%5C%0Ax%3D4%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%0A%5Cboxed%7BResposta%3A%7E%7ES%3D%5C%7B4%5C%7D%7D+++++ "2^{x}= \frac{144}{9}\\\\\\
2^{x}=16\\\\\
2^{x}=2^{4}\\\\\\\
x=4\\\\\\\\\\\
\boxed{Resposta:~~S=\{4\}}")
Boa tarde!
Bons estudos!
Solução!
Boa tarde!
Bons estudos!
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