$\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 number of solution $(s)$ of the equation $log_7(2^x -1) + log_7(2^x -7) = 1$, 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 value of ${(0.05)^{{{\log }_{_{\sqrt {20} }}}(0.1 + 0.01 + 0.001 + ……)}}$ is
Solution set of inequality ${\log _{10}}({x^2} – 2x – 2) \le 0$ is
If $3^x=4^{x-1}$, then $x=$
$(A)$ $\frac{2 \log _3 2}{2 \log _3 2-1}$ $(B)$ $\frac{2}{2-\log _2 3}$ $(C)$ $\frac{1}{1-\log _4 3}$ $(D)$ $\frac{2 \log _2 3}{2 \log _2 3-1}$
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