Question

Alguém me ajuda com essa questão de exponenciais?

Answer 1

3.
2ˣ⁻¹ + 2ˣ + 2ˣ⁺² = $\frac{11}{4}$ 
2ˣ . 2⁻¹ + 2ˣ + 2ˣ . 2² = $\frac{11}{4}$
2ˣ . (2⁻¹ + 1 + 2² ) = $\frac{11}{4}$
2ˣ . ( $\frac{11}{2}$ ) = $\frac{11}{4}$
2ˣ = $\frac{11}{4} / \frac{11}{2}$
2ˣ = 1/2
2ˣ = 2⁻¹  ⇒ cancela as bases
x = - 1


4.
2ˣ + 2ˣ⁺¹ + 2ˣ⁺² = 7√2
2ˣ + 2ˣ . 2⁺¹ + 2ˣ . 2⁺² = 7√2
2ˣ . ( 1 + 2¹ + 2²) = 7√2
2ˣ . 7 = 7√2
2ˣ = 7√2 / 7
2ˣ = √2
2ˣ = 2 ^ 1/2  ⇒ cancela as bases
x = 1/2

Answer 2

vamos lá..

$2^{x-1}+2^x+2^{x+2}= \frac{11}{4} \\ \\ desmembrar \\ \\ 2^x.2^{-1}+2^x+2^x.2^2= \frac{11}{4} \\ \\ colocando~~2^x~~como~~fator~~comum \\ \\ 2^x(2^{-1}+1+2^2)= \frac{11}{4} \\ \\ 2^x( \frac{1}{2} +1+4)= \frac{11}{4} \\ \\ 2^x( \frac{1}{2} +5)= \frac{11}{4} \\ \\ 2^x( \frac{11}{2} )= \frac{11}{4} \\ \\ 2^x= \frac{11}{4} \div \frac{11}{2} \\ \\ 2^x= \frac{\not11}{\not4_2} \times \frac{\not2}{\not11} \\ \\ 2^x= \frac{1}{2} \\ \\ \not2^x=\not2^{-1} \\ \\ x=-1~~~~Letra~~C$