Algebra 2: Find the value

Question

Let X₁ and X₂ (X₁ < X₂) be two real solutions of the equation log₂ ((x+3)⁴)=2 + log₂ ((x+3)²). Find the value of x₁-3x₂. Use Ti-84 if possible.

Answer 1

log₂ ((x+3)⁴)=2 + log₂ ((x+3)²)

log₂ ((x+3)⁴) - log₂ ((x+3)²) = 2

log₂ ((x+3)⁴/ (x+3)²) = 2

log₂ ((x+3)²) = 2

(x+3)² = 2²

^{x + 3 = - 2. or. x + 3 = 2}

^{x = -5. Or. x = -1}

^{So x}₁ ^{= -5. or. x}₂ ^{= -1}

And ^x₁ ^{- 3 x}₂ = -5 - 3(-1) = -5 + 3 = -2