${\log _4}18$ is

The sum of all the natural numbers for which $\log_{(4-x)}(x^2 - 14x + 45)$ is defined is -

If $x = \log_{3} 5$ and $y = \log_{17} 25$,which one of the following is correct?

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 $\log _{27}(\log _3 x) = \frac{1}{3}$,then the value of $x$ is

If $\log_{a}b + \log_{b}c + \log_{c}a = 0$,where $a, b,$ and $c$ are positive real numbers different from $1$,then the value of $(\log_{a}b)^3 + (\log_{b}c)^3 + (\log_{c}a)^3$ is