Why not changing bases?

Algebra Level 5

If the real values of x which satisfy: \[ \frac{4}{\log_3 (x^2) -2} + \log_x (1/9) > 1\] are on the interval \(X = \left]a,b\right[\ U \left]c, d\right[\), find the value of \[ 3a+b+c+d. \]

Obs: a<b<c<d

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