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?

$a^{\log_b c} =c^{\log_b a}$
let $k= a^{log_b c}$
$\log k=\log( a^{\log_b c})$
$\log k=\log_b c \log a$
$\log k=\frac{\log c}{\log b} \log a$
$\log k=\frac{\log a}{\log b} \log c$
$\log k=\log_b a \log c$
$\log k=\log c^{\log_b a}$
substituting value of k
$\log a^{\log_b c}=\log c^{\log_b a} $
therefore
$a^{\log_b c} =c^{\log_b a}$
