# Math Help - Prove an equivalence?

1. ## Prove an equivalence?

Hey guys,

My math professor gave us a problem today that I have no clue how to solve.

For a,b&c> 0, prove that a^(logb(c)) = c^(logb(a)). Where b is the base.

Thanks for the help

2. ## Re: Prove an equivalence?

Originally Posted by Reefer
For a,b&c> 0, prove that a^(logb(c)) = c^(logb(a)). Where b is the base.
Let $y=\left(\log_ba\right)\left(\log_bc\right)$. Then $y=\log_b\left(a^{\log_bc}\right)$ and also $y=\log_b\left(c^{\log_ba}\right)$.