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

If $\log _k x \cdot \log _5 k = \log _x 5$,where $k \neq 1$ and $k > 0$,then the value of $x$ is:

If ${\log _{10}}x = y$,then ${\log _{1000}}{x^2}$ is equal to

The solution to the equation $4.9^{x - 1} = 3\sqrt{2^{2x + 1}}$ is

What is the number of real values of the parameter $k$ for which the equation $({\log _{16}}x)^2 - {\log _{16}}x + {\log _{16}}k = 0$ has exactly one solution,given that the coefficients are real?

The expression $\log_{a} x$ is defined for $(a > 0, a \neq 1)$ when: