Question

Please help me. 4^(x+1)+2^(x+1)+2^x-1=0

Answer 1

• x = -2

Explanation:

• 
  `4^(x+1)+2^(x+1)+2^x-1=0`
• 
  `4*2^(2x)+2*2^x+2^x-1=0`

• 2ˣ = t

• 4t² + 3t - 1 = 0
• 4t² + 4t - t - 1 = 0
• 4t(t + 1) - (t + 1) = 0
• (t + 1)(4t - 1) = 0
• t = -1 (discounted as 2ˣ can't be negative)
• t = 1/4

• 2ˣ = 1/4
• 2ˣ = 2⁻²
• x = -2