Question

How do you expand `ln ((sqrt(a)/bc))`?

Answer 1

`1/2 log(a) + log(c) - log(b)`.

Explanation:

You could write the argument of the logarithm as `sqrt(a) * c * 1/b`. This is useful because the logarithm of a product is the sum of the logarithms, so

`log(sqrt(a) * c * 1/b) = log(sqrt(a)) + log(c) + log(1/b)`

Now we use the rule which states that `log(a^b)=blog(a)`. Writing `sqrt(a)` as `a^{1/2}`, and `1/b` as `b^{-1}`, we get

`log(sqrt(a))=1/2log(a)`, and `log(1/b)=-log(b)`.