Jawaban:
D. 2⁻⁴
Penjelasan dengan langkah-langkah:
[(²logx²/4)/²logx] + ²log4x = 4/²logx .kali ²logx
²log(x²/4) + ²logx . ²log4x = 4
²logx² - ²log4 + ²logx(²logx + ²log4) = 4
2²logx - 2 + (²logx)² + 2²logx = 4
(²logx)² + 4(²logx) - 6 = 0
(²logx + 2)² = 6 + 4
²logx + 2 = (+/-)√10
²logx₁ = - 2 + √10
x₁ = 2exp(-2 + √10)
²logx₂ = -2 - √10
x₂ = 2exp(-2 -√10)
x₁ . x₂ = 2exp(-2 + √10) x 2exp(-2 - √10)
x₁ . x₂ = 2exp[(-2 + √10)+(-2 - √10)]
x₁ . x₂ = 2exp(- 4)
x₁ . x₂ = 2⁻⁴............(D)
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Jawaban:
D. 2⁻⁴
Penjelasan dengan langkah-langkah:
[(²logx²/4)/²logx] + ²log4x = 4/²logx .kali ²logx
²log(x²/4) + ²logx . ²log4x = 4
²logx² - ²log4 + ²logx(²logx + ²log4) = 4
2²logx - 2 + (²logx)² + 2²logx = 4
(²logx)² + 4(²logx) - 6 = 0
(²logx + 2)² = 6 + 4
²logx + 2 = (+/-)√10
²logx₁ = - 2 + √10
x₁ = 2exp(-2 + √10)
²logx₂ = -2 - √10
x₂ = 2exp(-2 -√10)
x₁ . x₂ = 2exp(-2 + √10) x 2exp(-2 - √10)
x₁ . x₂ = 2exp[(-2 + √10)+(-2 - √10)]
x₁ . x₂ = 2exp(- 4)
x₁ . x₂ = 2⁻⁴............(D)