If 2^{x + 3} + 2^{x + 1} = 320, then x =

1. 2

2. 3

3. 4

4. 5

Given,

2^{(x + 3)} + 2^{(x + 1)} = 320

Simplifying the expression:

$\Rightarrow 2^{x + 1 + 2} + 2^{x + 1} = 320 \\[1em] \Rightarrow 2^{x + 1} \times 2^2 + 2^{x + 1} = 320 \\[1em] \Rightarrow 2^{x + 1} \Big(2^2 + 1\Big) = 320 \\[1em] \Rightarrow 2^{x + 1} \times 5 = 320 \\[1em] \Rightarrow 2^{x + 1} = \dfrac{320}{5} \\[1em] \Rightarrow 2^{x + 1} = 64 \\[1em] \Rightarrow 2^{x + 1} = 2^6$

Equating the exponents:

⇒ x + 1 = 6

⇒ x = 6 - 1

⇒ x = 5.

Hence, option 4 is the correct option.