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To simplify this let x=3^y, then 3x²-4x+1=0=(3x-1)(x-1)=0, so x=⅓ or x=1.

Therefore, 3^y=⅓=3⁻¹, and y=-1; or 3^y=1=3⁰, and y=0.

Solution: y=0 or -1.

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