Exponents

$\text{Which of the following are greater than } x \text{ when } x=\frac{9}{11}?$ $(I)\ \frac{1}{x}$ $(II)\ \frac{x+1}{x}$ $(III)\ \frac{x+1}{x-1}$

Find the value of $x$, if: $\left( 2^{\frac{1}{\log_x 4}} \right) \left( 2^{\frac{1}{\log_x 16}} \right) \left( 2^{\frac{1}{\log_x 256}} \right) \cdots = 2$

Number of distinct integer values of $a$ satisfying $2^{2a} - 3(2^{a+2}) + 25 = 0$ is:

If $x < -1$ and $2^{|x+1|} - 2^x = |2x - 1| + 1$ then the value of $x$ is:

Let: $ X = 2^{100},\quad Y = 3^{100},\quad Z = 4^{100} $ Which statement is true?