Solve : 8 × 2^2x + 4 × 2^{x + 1} = 1 + 2^x

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KnowledgeBoat · Accepted Answer

Given, ⇒ 8 × 2^2x + 4 × 2^{x + 1} = 1 + 2^x ⇒ 8 × 2^(x)(2) + 4 × 2^x.2¹ = 1 + 2^x Substituting 2^x = a, in above equation, we get : ⇒ 8 × a² + 4a × 2 = 1 + a ⇒ 8a² + 8a = 1 + a ⇒ 8a² + 8a - a - 1 = 0 ⇒ 8a(a + 1) - 1(a + 1) = 0 ⇒ (8a - 1)(a + 1) = 0 ⇒ 8a - 1 = 0 or a + 1 = 0 ⇒ 8a = 1 or a = -1 a cannot be negative as 2^x, for any value of x is greater than 0. ⇒ 8(2^x) = 1 ⇒ 2^x = ⇒ ⇒ 2^x = 2^-3 ⇒ x = -3. Hence, x = -3.

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Solve :
8 × 2^2x + 4 × 2^{x + 1} = 1 + 2^x

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