Logarithmic Inequalities

Sum of all integral values of $c$ for which the inequality $1+{\log }_2\left(2x^2+2x+\frac{7}{2}\right)\ge {\log }_2\left(c{x}^2+c\right)$ has at least one solution, is

Complete solution set of the inequality $\sqrt{{\log }_{10}^{2}x-1}>{\log }_{10}x-1$ is

Exhaustive set of values of $x$ satisfying ${\log }_{\left|x\right|}\left(x^2+x+1\right)\ge 0$ is

If the solution set of the inequality ${\log }_{\sqrt{0.9}}{\log }_5\left(\sqrt{x^2+5+x}\right)>0$ contains $n$ integral values, then $n$ equals to

If ${\log }_{0.5}{\log }_5\left(x^2-4\right)>{\log }_{0.5}1,$ then $x$ lies in the interval