$7\log \left( {{{16} \over {15}}} \right) + 5\log \left( {{{25} \over {24}}} \right) + 3\log \left( {{{81} \over {80}}} \right)$ is equal to

The set of real values of $x$ for which ${\log _{0.2}}{{x + 2} \over x} \le 1$ is

If $x = {\log _3}5,\,\,\,y = {\log _{17}}25,$ which one of the following is correct

Solution set of inequality ${\log _{10}}({x^2} - 2x - 2) \le 0$ is

The value of $\left(\left(\log _2 9\right)^2\right)^{\frac{1}{\log _2\left(\log _2 9\right)}} \times(\sqrt{7})^{\frac{1}{\log _4 7}}$ is. . . . . . .

The number of integral solutions $x$ of $\log _{\left(x+\frac{7}{2}\right)}\left(\frac{x-7}{2 x-3}\right)^2 \geq 0$ is