$\frac{\log \sqrt{8}}{\log 8}$ is equal to

If $\log _{8} p=2.5$ and $\log _{2} q=5$,then $p$ in terms of $q$ is

If $\frac{\log x}{a^{2}+a b+b^{2}}=\frac{\log y}{b^{2}+b c+c^{2}}=\frac{\log z}{c^{2}+c a+a^{2}}$,then $x^{a-b} \cdot y^{b-c} \cdot z^{c-a}=$

If $y = \frac{1}{a^{1-\log _{a} x}}$,$z = \frac{1}{a^{1-\log _{a} y}}$ and $x = a^{k}$,then $k =$

If $4^{x} + 2^{2x-1} = 3^{x+\frac{1}{2}} + 3^{x-\frac{1}{2}},$ then $x =$

If $\log 2=x, \log 3=y$ and $\log 7=z,$ then the value of $\log (4 \sqrt[3]{63})$ is