The value of $\left(\frac{1}{\log _{3} 12}+\frac{1}{\log _{4} 12}\right)$ is

The number of integers satisfying the inequality $\sqrt {{{\log }_3}(x) - 1} + \frac{{\frac{1}{2}{{\log }_3}({x^3})}}{{{{\log }_3}(\frac{1}{3})}} + 2 > 0$ is

If $\log _3 x+\log _3 y=2+\log _3 2$ and $\log _3(x+y)=2$, then

If $\log _{(3x-1)}(x-2) = \log _{(9x^2-6x+1)}(2x^2-10x-2)$,then $x$ equals

If $\log_2 x + \log_x 2 = \frac{10}{3} = \log_2 y + \log_y 2$ and $x \neq y$,then $x + y = $

The number of solutions of the equation $\log _{4}(x-1)=\log _{2}(x-3)$ is