The number $\log_{20} 3$ lies in

If $\log _{2} 6 + \frac{1}{2x} = \log _{2} (2^{\frac{1}{x}} + 8)$, then the values of $x$ are

If $\log _k x \cdot \log _5 k = \log _x 5$,where $k \ne 1$ and $k > 0$,then $x$ is equal to:

If $\log _{1/\sqrt{2}} \sin x > 0$ for $x \in [0, 4\pi]$,find the number of values of $x$ that are integer multiples of $\frac{\pi}{4}$.

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

If $x+\log _{10}\left(1+2^{x}\right)=x \log _{10} 5+\log _{10} 6$, then the value of $x$ is