The value of $\frac{\log_{3} 5 \times \log_{25} 27 \times \log_{49} 7}{\log_{81} 3}$ is

If $a^x = b^y = c^z = d^w$, the value of $x\left(\frac{1}{y} + \frac{1}{z} + \frac{1}{w}\right)$ is

Let $x$ and $y$ be real numbers such that $x > 2y > 0$ and $2 \log (x - 2y) = \log x + \log y$. Then,the possible value$(s)$ of $\frac{x}{y}$ is/are:

The roots of the equation $2^{x + 2} \cdot 27^{x/(x - 1)} = 9$ are given by

The value of $(0.16)^{\log _{2.5}\left(\frac{1}{3}+\frac{1}{3^{2}}+\frac{1}{3^{3}}+\ldots \infty\right)}$ is equal to

If $\frac{1}{\log_3 \pi} + \frac{1}{\log_4 \pi} > x$,then $x =$ ?