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

The set of real values of $x$ for which $2^{\log_{\sqrt{2}}(x - 1)} > x + 5$ is

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

If $x = \log_{5}(1000)$ and $y = \log_{7}(2058)$,then:

Let $n$ be a positive integer such that $\log _2 \log _2 \log _2 \log _2 \log _2(n) < 0 < \log _2 \log _2 \log _2 \log _2(n)$. Let $l$ be the number of digits in the binary expansion of $n$. Then the minimum and the maximum possible values of $l$ are

If $A = \log_2 \log_2 \log_4 256 + 2 \log_{\sqrt{2}} 2$,then the value of $A$ is: