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Q.
The expression a $a^{\frac{\log (\log a)}{\log a}}$ where all logarithm are taken to the base b is equal to
Continuity and Differentiability
Solution:
$ a ^{\log _{ b }\left(\log _{ b } a \right) \cdot \log _{ a } b } $
$\text { Let } \log _{ b } a = m$
$a ^{\log _{ b } m \cdot \log _{ a } b }= a ^{\log _{ a } m } \Rightarrow m =\log _{ b } a$