Inequality with log

Algebra Level 3

log4log3log2(x2+7x)0\large \log_4 \log_3 \log_2 \left(x^2 + 7x\right) \geq 0

If the ranges of real number xx are (,a][b,)(-\infty,a] \cup [b,\infty), where aa and bb are integers, then find ab\dfrac{a}{b}.

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