If ${\log _{0.3}}(x - 1) < {\log _{0.09}}(x - 1),$ then $x$ lies in the interval
$(2,\infty )$
$(-2, -1)$
$(1, 2)$
None of these
Which is the correct order for a given number $\alpha $in increasing order
If ${\log _7}2 = m,$ then ${\log _{49}}28$ is equal to
The value of $(0.16)^{\log _{2.5}\left(\frac{1}{3}+\frac{1}{3^{2}}+\frac{1}{3^{3}}+\ldots . to \infty\right)}$ is equal to
If ${\log _5}a.{\log _a}x = 2,$then $x$ is equal to
The set of real values of $x$ for which ${\log _{0.2}}{{x + 2} \over x} \le 1$ is