What is x if lg^2 x^3 - 6lg x + 1 = 0 ?

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We have to solve for x : (lg x^3)^2  - 6* lg x + 1 = 0

(lg x^3)^2  - 6* lg x + 1 = 0

=> (3 lg x)^2 - 6 lg x + 1 = 0

=> 9 (lg x)^2 - 6 lg x + 1 = 0

let lg x = y

=> 9y^2 - 6y + 1 = 0

=> ( 3y - 1)^2 = 0

=> 3y - 1...

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