Question

Simplify for x: (root 3)^3x-4= 3x (root 27^x)

Answer 1

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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