What's with these logs?

Algebra Level 3

\[ \ln\left(2x^{2} - 3x + 8\right) \le \dfrac{\ln\left(x^{4}+4x^{3} + 8x^{2} + 8x + 4\right)}{2} \]

Find the product of all integer values of \( x \) which satisfy the inequality above.

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