6.45 If $a>1, \quad b>1, \quad p=\frac{\log _{b}\left(\log _{b} a\right)}{\log _{b} a}$, then $a^{p}$ equals
(A) 1.
(B) $b$.
(C) $\log _{a} b$.
(D) $\log _{b} a$.
(E) $a \log _{b} a$.
(33rd American High School Mathematics Examination, 1982)
[Solution] From the given, we have $p\left(\log _{b} a\right)=\log _{b}\left(\log _{b} a\right)$, which means $\log _{b}\left(a^{p}\right)=\log _{b}\left(\log _{b} a\right)$.

Therefore, $a^{p}=\log _{b} a$.
Hence, the correct choice is $(D)$.