${\log _7}{\log _7}\sqrt {7(\sqrt {7\sqrt 7 } )} = $

Let $S$ be the sum of the digits of the number $15^2 \times 5^{18}$ in base $10$. Then,

The number of solution of ${\log _2}(x + 5) = 6 - x$ is

The value of $(0.16)^{\log _{2.5}\left(\frac{1}{3}+\frac{1}{3^{2}}+\frac{1}{3^{3}}+\ldots . to \infty\right)}$ is equal to

If ${\log _{0.3}}(x - 1) < {\log _{0.09}}(x - 1)$ then $x \ne 1$ lies in

Let $x, y$ be real numbers such that $x>2 y>0$ and $2 \log (x-2 y)=\log x+\log y$  Then, the possible value(s) of $\frac{x}{y}$