Can anyone explain step by step the relation between the logs of a number to different bases?

If we take a number x and do the following:

$\displaystyle log_{a}x$

then

$\displaystyle log_{b}x$

What is the relationship of the two?

I believe the formula that sums the relationship is:

$\displaystyle log_{b}x log_{a}x=log_{b}x$

Can anyone explain how this is reached?

P.S sorry for the formatting!