5.1. Find the sum of all integer values of the argument $x$ for which the corresponding values of the function

$$
y=x^{2}+x\left(\log _{2} 18-\log _{3} 12\right)-\log _{3} 16-4 \log _{2} 3
$$

do not exceed 8.
Solution. Let $a=\log _{2} 3$. Then the condition of the problem will turn into the inequality

$$
x^{2}+2\left(a-\frac{1}{a}\right) x-4\left(a+\frac{1}{a}+2\right) \leqslant 0
$$

Considering that $a \in\left(\frac{3}{2}, 2\right)$, we get $x \in\left[-2 a-2, \frac{2}{a}+2\right]$. Since $-6<-2 a-2<-5.3<\frac{2}{a}+2<4$, the integer solutions will be the numbers $-5,-4,-3,-2,-1,0,1,2,3$.

Answer: -9 . (A)

![](https://cdn.mathpix.com/cropped/2024_05_06_a8c31eb257d724803ce6g-06.jpg?height=67&width=721&top_left_y=1094&top_left_x=719)