Please answer with detail all the questions within 10 hours.:


1. $$\begin{gathered} \mathrm{If} \frac{1}{{\log }_2\mathrm{\pi }}+\frac{1}{{\log }_4\mathrm{\pi }}>\mathrm{k} \mathrm{than} \mathrm{the} \mathrm{value} \mathrm{of} \mathrm{k} \mathrm{is} \mathrm{where} \mathrm{k} \mathrm{is} \mathrm{any} \mathrm{integer}. \\ \left(\mathrm{A}\right) 1 \left(\mathrm{B}\right) 2 \left(\mathrm{C}\right)\hspace{0.17em}3 \left(\mathrm{D}\right) 4 \\ 2. \mathrm{If} {\log }_{4}5=\mathrm{x} \mathrm{and} {\log }_{5}6=\mathrm{y}, \mathrm{then}. \\ \left(\mathrm{A}\right) {\log }_{4}6=\mathrm{xy}, \left(\mathrm{B}\right) {\log }_{6}4=\mathrm{xy} \left(\mathrm{C}\right) {\log }_{3}2=\frac{1}{2\mathrm{xy}-1} \left(\mathrm{D}\right) {\log }_{2}3=\frac{1}{2\mathrm{xy}-1} \end{gathered}$$