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 $\dfrac{a}{b}$ .