Question

How to simplify logarithms that are divided by each other?

Answer 1

If the logarithms has that same base, therefore you can use:

$\dfrac{\log_ab}{\log_ac}=\log_cb,\ where\ a,\ b,\ c > 0\ and\ a\neq1\ and\ c\neq1$

Example

$\dfrac{\log_29}{\log_23}=\log_39=2$

I hope I helped :)