Simplify for x: (root 3)^3x-4= 3x (root 27^x)
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Given : (√3)³ˣ⁻⁴ = 3x (√27)ˣ
To Find : Value of x
Solution:
(√3)³ˣ⁻⁴ = 3x (√27)ˣ
=> (√3)³ˣ⁻⁴ = 3x (√3³)ˣ
=> (√3)³ˣ⁻⁴ = 3x (√3 )³ˣ
(xᵃ)ᵇ = xᵃᵇ
=> (√3)³ˣ⁻⁴ = x√3² (√3 )³ˣ
xᵃ.xᵇ=xᵃ⁺ᵇ
=> (√3)³ˣ⁻⁴ = x(√3 )³ˣ⁺²
=> (√3)⁻⁶ = x
=> (√3²)⁻³ = x
=> 3⁻³ = x
=> 1/3³ = x
=> x = 1/27
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