Question

How do you expand `log_3((uv^2)/w)`?

Answer 1

So `log_3((uv^2)/w) -> (log_3(u)+2log_3(v))/log_3(w)`

Explanation:

If source values are multiplied the logs are added
`" " log(ab) -> log(a)+log(b)`

Is source values are divided the logs are subtracted.
`" "log(a/b)->log(a)-log(b)`

If source values are raised to some power then the log is multiplied by the value of the power
`" "log(a^4)->4log(a)`

If source value are rooted then the log is divided by the value of that root
`" "log(root(5)(a))-> 1/5log(a)`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

So `log_3((uv^2)/w) -> (log_3(u)+2log_3(v))/log_3(w)`