The value of $\sqrt{(\log_{0.5} 4)^2}$ is

If $n = (2020)!$,then the value of $\frac{1}{\log _{2} n} + \frac{1}{\log _{3} n} + \frac{1}{\log _{4} n} + \ldots + \frac{1}{\log _{2020} n}$ is equal to:

Let $\phi (x) = x + 2^{\log_x 3} - 3^{\log_x 2}$. Then which of the following is true?

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:

If $x$ satisfies the inequality $\log _{25} x^2 + (\log _5 x)^2 < 2$, then $x$ belongs to

$A$ real root of the equation $\log_{4}\{\log_{2}(\sqrt{x + 8} - \sqrt{x})\} = 0$ is