Simplyfing Log Question

Question

Don't know the concepts of diving and multiplying whole logs.

$\frac{\log _a\left(x\right)}{\log _a\left(y\right)}\cdot \frac{\log _b\left(y\right)}{\log _b\left(x\right)}$

Can you please tell me how to simplify this?

Answer 1

Use $\displaystyle\log_ba=\frac{\log_ca}{\log_cb}$ where $c$ is arbitrary real positive number and real $a,b>0$