Logarithmic Inequality

Algebra Level 5

\[ \Large f(x) = x \log_{\log_{|x^2 - 3 | - 2 } (x^2 - 3|x| + 2) } \left( \dfrac{x^3 - |3x+2|}{x^3 - |3x-2|}\right) \]

If the solution to \(f(x) \geq 0 \) consists of the union of \(n\) intervals, find \(n\).

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