Why $\log xy=\log x+\log y$? It is of course well known and basic formula. I am just curious. Is there a proof for it?
How to prove that $\log xy=\log x+\log y$?

$$e^{\ln(x)+\ln(y)}=e^{\ln(x)}e^{\ln(y)}=xy$$ so $$\ln(xy)=\ln(x)+\ln(y)$$
As noted in the comments, this works for any log. I used base $e$ out of habit/convenience.
