If 4 × 2^{x + 3} = 8^{x + 1}, then 2^x =

1. 1

2. 2

3. 4

4. 8

Given,

⇒ 4 × 2^{x + 3} = 8^{x + 1}

Simplifying the expression,

$\Rightarrow 4 \times 2^{x + 3} = (2^3)^{x + 1} \\[1em] \Rightarrow 4 \times 2^{x + 3} = 2^{3x + 3} \\[1em] \Rightarrow 4 = \dfrac{2^{3x + 3}}{2^{x + 3} } \\[1em] \Rightarrow 2^2 = 2^{3x + 3} \times 2^{-(x + 3)} \\[1em] \Rightarrow 2^2 = 2^{3x + 3 - (x + 3)} \\[1em] \Rightarrow 2^2 = 2^{3x - x + 3 - 3} \\[1em] \Rightarrow 2^2 = 2^{2x}$

Equating the exponents:

⇒ 2 = 2x

⇒ x = $\dfrac{2}{2}$

⇒ x = 1.

⇒ 2^x = 2¹ = 2.

Hence, option 2 is the correct option.