If ${a^2} + 4{b^2} = 12ab,$ then $\log (a + 2b)$ is
${1 \over 2}[\log a + \log b - \log 2]$
$\log {a \over 2} + \log {b \over 2} + \log 2$
${1 \over 2}[\log a + \log b + 4\log 2]$
${1 \over 2}[\log a - \log b + 4\log 2]$
The number ${\log _2}7$ is
The set of real values of $x$ satisfying ${\log _{1/2}}({x^2} - 6x + 12) \ge - 2$ is
The set of real values of $x$ for which ${\log _{0.2}}{{x + 2} \over x} \le 1$ is
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. . . . . . .