# 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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