If $\log _2 x + \log _4 x + \log _8 x + \log _{16} x = \frac{25}{36}$ and $x = 2^k$,then $k$ is

$\text{If } \log _{0.2}(x-1) > \log _{0.04}(x+5), \text{ then }$

If $y = 2^{1/\log_x 4}$,then $x$ is equal to

The solution set of the equation $\left| {1 - {{\log }_{1/6}}x} \right| + \left| {{{\log }_2}x} \right| + 2 = \left| {3 - {{\log }_{1/6}}x + {{\log }_{1/2}}x} \right|$ is $\left[ {\frac{a}{b},a} \right]$,where $a, b \in N$. Then the value of $(a + b)$ is:

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

Consider all natural numbers whose decimal expansion has only the even digits $0, 2, 4, 6, 8$. Suppose these are arranged in increasing order. If $a_n$ denotes the $n$-th number in this sequence,then $\frac{\lim_{n \rightarrow \infty} \log a_n}{\log n}$ equals