Question

Sobre inequação exponencial:

1) Determine a solução:

$2 \leq 2^{x+1} \leq 16$

Answer 1

Trata-se de uma inequação simultânea.
 Na prática são duas inequações
Veja

                    $2 \leq 2^{x+1} \leq 16 \\ \\ 2^1 \leq 2^{x+1} \leq 2^4$

     Sendo as bases iguais

                    1 < x + 1 < 4
                                             1 < x + 1
                                              - x < 1 - 1
                                                                           x > 0      S1

                                             x + 1 < 4
                                             x < 4 -1
                                                                           x < 3      S2
         S = S1 S2
Na reta numérica

                                 ___0___________________3_______
                                        |     x > 0                 x < 3 |
                                                        
                                                        S = { x∈R| 0 < x < 3 }

Answer 2

Ola Mailer

2 ≤ 2^(x + 1)

2 ≤ 2^(0 + 1)

2^(x + 1) ≤ 16
2^(3 + 1) ≤ 16

0 ≤ x ≤ 3

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