Hướng dẫn giải:

Đáp án C.

Điều kiện:  \( \left\{ \begin{align}& x>0 \\ & {{\log }_{8}}x>0 \\ & {{\log }_{2}}x>0 \\ \end{align} \right. \)

Ta có:  \( {{\log }_{2}}\left( {{\log }_{8}}x \right)={{\log }_{8}}\left( {{\log }_{2}}x \right) \) \( \Leftrightarrow {{\log }_{2}}\left( \frac{1}{3}{{\log }_{2}}x \right)={{\log }_{2}}{{\left( {{\log }_{2}}x \right)}^{\frac{1}{3}}} \)

 \( \Leftrightarrow \frac{1}{3}{{\log }_{2}}x=\sqrt[3]{{{\log }_{2}}x}\Leftrightarrow {{\log }_{2}}x=3\sqrt[3]{{{\log }_{2}}x} \) (*)

Đặt  \( t=\sqrt[3]{{{\log }_{2}}x}\left( t>0 \right)\Rightarrow {{t}^{3}}={{\log }_{2}}x  \)

 \( (*)\Leftrightarrow {{t}^{3}}=3t\Leftrightarrow \left[ \begin{align} & t=0 \\  & t=\sqrt{3} \\ & t=-\sqrt{3} \\ \end{align} \right. \) \( \Rightarrow t=\sqrt{3}\Rightarrow \sqrt[3]{{{\log }_{2}}x}=\sqrt{3}\Leftrightarrow {{\log }_{2}}x=3\sqrt{3} \)

 \( \Leftrightarrow {{\log }_{2}}x=3\sqrt{3}\Leftrightarrow x={{2}^{3\sqrt{3}}} \) (thỏa mãn đề bài).

Vậy  \( P={{\left( 3\sqrt{3} \right)}^{4}}=729 \) .