Inequality with log

Algebra Level 3

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

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