Question

qual o valor de x torna verdadeira a inequação 2^x+1 + 2^x-2=1/2 é?

Answer 1

$2^{x+1} + 2^{x-2}=\frac{1}{2}\\\\ 2.2^x+\frac{2^x}{4}=\frac{1}{2}\\\\\boxed{m=2^x}\\\\2m+\frac{m}{4}=\frac{1}{2}\\\\8m+m=2\\\\9m=2\\\\m=\frac{9}{2}\\\\2^x=\frac{9}{2}\\\\log2^x=log{\frac{9}{2}}\\\\x.log2=log{\frac{9}{2}}\\\\\boxed{x=\frac{log{\frac{9}{2}}}{log2}}$