E-8 10'09, (log, (log, x)) = 1 and log, (log, (log, x)) = 0 then 'p' equals (A) rar (B) rg (C) 1 (D)rla

$$\begin{gathered} {10}^{\log p\left({\log }_q\right(\log x\left)\right)}=1 \\ \Rightarrow {\log }_p\left({\log }_q\right({\log }_{r}x\left)\right)=0 \\ \Rightarrow {\log }_q\left({\log }_{r}x\right)=1 \\ \Rightarrow {\log }_{r}x=q \Rightarrow x=r^q ....1 \\ {\log }_q\left({\log }_r\right({\log }_{p}x\left)\right)=0 \\ \Rightarrow {\log }_r\left({\log }_{p}x\right)=1 \\ \Rightarrow {\log }_{p}x=r \\ \Rightarrow x=p^r .....2 \\ form \left(1\right) \& 2 \\ {r}^q=p^r \\ q\log r=r\log p \\ \Rightarrow \log p=\frac{q}{r}\log r=\log r^{q/r} \\ \mathbf{\Rightarrow }\mathit{p}\mathbf{=}{\mathit{r}}^{\mathbf{q}\mathbf{/}\mathbf{r}} \\ \mathit{O}\mathit{p}\mathit{t}\mathit{i}\mathit{o}\mathit{n}\mathbf{ }\mathbf{\left(}\mathbf{1}\mathbf{\right)} \end{gathered}$$