$\sum\limits_{r = 1}^{89} {{{\log }_3}(\tan \,\,{r^o})} = $
$3$
$1$
$2$
$0$
(d) $\sum\limits_{r = 1}^{39} {{{\log }_3}(\tan {r^o}) = {{\log }_3}(\tan {{45}^o}} ) = {\log _3}1 = 0$.
The value of $\sqrt {(\log _{0.5}^24)} $ is
The set of real values of $x$ for which ${2^{{{\log }_{\sqrt 2 }}(x – 1)}} > x + 5$ is
If ${a^2} + 4{b^2} = 12ab,$ then $\log (a + 2b)$ is
The sum of all the natural numbers for which $log_{(4-x)}(x^2 -14x + 45)$ is defined is –
If ${\log _k}x.\,{\log _5}k = {\log _x}5,k \ne 1,k > 0,$ then $x$ is equal to
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