If ${\log _{0.04}}(x - 1) \ge {\log _{0.2}}(x - 1)$ then $x$ belongs to the interval
$\left( {1,\,\,2} \right]$
$\left( { - \infty ,\,2} \right]$
$\left[ {2, + \,\infty } \right)$
None of these
The number of solution pairs $(x, y)$ of the simultaneous equations $\log _{1 / 3}(x+y)+\log _3(x-y)=2$ $2^{y^2}=512^{x+1}$ is
The set of real values of $x$ for which ${\log _{0.2}}{{x + 2} \over x} \le 1$ is
The solution of the equation ${\log _7}{\log _5}$ $(\sqrt {{x^2} + 5 + x} ) = 0$
If $x = {\log _3}5,\,\,\,y = {\log _{17}}25,$ which one of the following is correct
The value of $6+\log _{\frac{3}{2}}\left(\frac{1}{3 \sqrt{2}} \sqrt{4-\frac{1}{3 \sqrt{2}} \sqrt{4-\frac{1}{3 \sqrt{2}} \sqrt{4-\frac{1}{3 \sqrt{2}} \ldots}}}\right)$ is