Respostas

2014-07-22T19:27:34-03:00
Olá Suelen,

use a propriedade da exponenciação:

a^{m+n}~\to~a^m*a^n\\\\ a^{-1}~\to~\dfrac{1}{a^1}~\to~\dfrac{1}{a}

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2^{x+2}+2^{x-1}=18\\
2^x*2^2+2^x*2^{-1}=18\\\\
2^x~em~evidencia:\\\\
2^x*(2^2+2^{-1})=18\\
2^x*\left(4+ \dfrac{1}{2}\right)=18\\\\
2^x* \dfrac{9}{2}=18\\\\
2^x*9=2*18\\
2^x*9=36\\\\
2^x= \dfrac{36}{9}\\\\
2^x=4\\
2^x=2^2\\
\not2^x=\not2^2\\\\
x=2\\\\
\boxed{S=\{2\}}

Tenha ótimos estudos =))