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

The equation $x^{(\log _{3} x)^{2}-\frac{9}{2} \log _{3} x+5}=3 \sqrt{3}$ has

If $\log _{1/\sqrt{2}} \sin x > 0$ for $x \in [0, 4\pi]$,then the number of values of $x$ which are integral multiples of $\frac{\pi}{4}$ is:

If $A = \log _2 \log _2 \log _4 256 + 2 \log _{\sqrt{2}} 2$,then $A$ is equal to

If $\log_{5} a \cdot \log_{a} x = 2$,then $x$ is equal to

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