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

The value of $x$ in the given equation $4^x - 3^{x - 1/2} = 3^{x + 1/2} - 2^{2x - 1}$ is

In a right-angled triangle, the sides are $a, b$ and $c$, with $c$ as the hypotenuse, and $c-b \neq 1, c+b \neq 1$. Then the value of $\frac{\log_{c+b} a + \log_{c-b} a}{2 \log_{c+b} a \times \log_{c-b} a}$ is:

The number of solutions of $\frac{\log 5 + \log (x^2 + 1)}{\log (x - 2)} = 2$ is

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

If $\frac{\log x}{b - c} = \frac{\log y}{c - a} = \frac{\log z}{a - b}$,then which of the following is true?