The value of $0.\overline{234}$ is

If $x, y$ are real numbers such that $3^{(x/y)+1} - 3^{(x/y)-1} = 24$,then the value of $(x+y)/(x-y)$ is

If $a, b, c$ are digits,then the rational number represented by $0.cababab...$ is:

If for $x \in \left(0, \frac{\pi}{2}\right)$,$\log_{10} \sin x + \log_{10} \cos x = -1$ and $\log_{10}(\sin x + \cos x) = \frac{1}{2}(\log_{10} n - 1)$,$n > 0$,then the value of $n$ is equal to

The value of ${81^{(1/{\log_5}3)}} + {27^{\log_9 36}} + {3^{4/{\log_7}9}}$ is

If ${2^x} = {4^y} = {8^z}$ and $xyz = 288$,then find the value of $\frac{1}{{2x}} + \frac{1}{{4y}} + \frac{1}{{8z}}$.