Logarithm proof problem: $a^{\log_b c} = c^{\log_b a}$ I have been hit with a homework problem that I just have no idea how to approach. Any help from you all is very much appreciated. Here is the problem
Prove the equation: $a^{\log_b c} = c^{\log_b a}$
Any ideas?

$\large{a^{\log_b c}=e^{\ln a \cdot\log_b c}= e^{\ln a\cdot\ln c/\ln b}}=c^{\ln a/\ln b}=c^{\log_b a}$.
