Solution set of inequality ${\log _{10}}({x^2} - 2x - 2) \le 0$ is
$[ - 1,\,1 - \sqrt 3 ]$
$[1 + \sqrt 3 ,3]$
$[ - 1,\,1 - \sqrt 3 ) \cup (1 + \sqrt 3 \,,\,3]$
None of these
The value of ${\log _2}.{\log _3}....{\log _{100}}{100^{{{99}^{{{98}^{{.^{{.^{{{.2}^1}}}}}}}}}}}$ is
If $\log x:\log y:\log z = (y - z)\,:\,(z - x):(x - y)$ then
Let $a=3 \sqrt{2}$ and $b=\frac{1}{5^{\frac{1}{6}} \sqrt{6}}$. If $x, y \in R$ are such that $3 x+2 y=\log _a(18)^{\frac{5}{4}} \text { and }$ $2 x-y=\log _b(\sqrt{1080}),$ then $4 x+5 y$ is equal to. . . .
If ${a^2} + 4{b^2} = 12ab,$ then $\log (a + 2b)$ is
The value of ${(0.05)^{{{\log }_{_{\sqrt {20} }}}(0.1 + 0.01 + 0.001 + ......)}}$ is