How is $\ a^{\log_nb} = b^{\log_na} $ ?
I know this is likely a trivial identity but I don't see how the statements are equivalent.
I came across this equivalence in Chapter 4.4 of Introduction to Algorithms, CLRS
How is $\ a^{\log_nb} = b^{\log_na} $?
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logarithms
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3Take $\log_n$ of both sides. – 2017-02-07
1 Answers
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Rewrite $a$ as $n^{log_n(a)}$, then $a^{log_n(b)}=n^{log_n(a)log_n(b)}$. Same for the right hand side, $b^{log_n(a)}=n^{log_n(b)log_n(a)}$.