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Problem of the day

If $a>1, b>1$, and $p=\frac{\log_b(\log_ba)}{\log_ba}$, then $a^p$ equals

$\textbf {(A)}\ 1 \qquad  \textbf {(B)}\ b \qquad  \textbf {(C)}\ \log_ab \qquad  \textbf {(D)}\ \log_ba \qquad  \textbf {(E)}\ a^{\log_ba}$

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