The value of $\left(\frac{1}{\log _{3} 12}+\frac{1}{\log _{4} 12}\right)$ 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

The number of solutions of the equation $\log _{(x+1)}(2 x^{2}+7 x+5)+\log _{(2 x+5)}(x+1)^{2}-4=0$ for $x > 0$ is:

${\log _4}18$ is

If $x_n > x_{n-1} > \dots > x_2 > x_1 > 1$,then the value of $\log_{x_1} \log_{x_2} \log_{x_3} \dots \log_{x_n} (x_n^{x_{n-1}^{\dots^{x_1}}})$ is:

Let $k>0$ and $t=\operatorname{sech}^{-1}\left(\frac{1}{2}\right)-\operatorname{cosech}^{-1}\left(\frac{3}{k}\right)$. If $3 e^t=2+\sqrt{3}$,then $k=$