Es $n^{\log c} = c^{\log n}$ verdad?

Question

Es $n^{\log c}$ el mismo que $c^{\log n}$? Si es así, por favor explique.

Answer 1

$$ n^{\log_b c} = \Big(b^{\log_b n}\Big)^{\log_b c} = b^{(\log_b n)(\log_b c)} = \Big(b^{\log_b c}\Big)^{\log_b n} = c^{\log_b n}. $$