The set of real values of $x$ that satisfy the inequality ${\log _{1/2}}({x^2} - 6x + 12) \ge - 2$ is:

The value of $\log _{3}4 \cdot \log _{4}5 \cdot \log _{5}6 \cdot \log _{6}7 \cdot \log _{7}8 \cdot \log _{8}9$ is

The equation $x^{(\log _{3} x)^{2}-\frac{9}{2} \log _{3} x+5}=3 \sqrt{3}$ has

If $x_n > x_{n-1} > \dots > x_2 > x_1 > 1$,then the value of $\log_{x_1} \log_{x_2} \log_{x_3} \dots \log_{x_n} (x_n^{x_{n-1}^{\dots^{x_1}}})$ is:

Let $a = 3 \sqrt{2}$ and $b = \frac{1}{5^{\frac{1}{6}} \sqrt{6}}$. If $x, y \in \mathbb{R}$ are such that $3x + 2y = \log_a(18)^{\frac{5}{4}}$ and $2x - y = \log_b(\sqrt{1080})$,then $4x + 5y$ is equal to:

The set of real values of $x$ satisfying $\log _{1/2}(x^2 - 6x + 12) \ge -2$ is