Question

How do you expand `ln(sqrt(((xy^2)/z))`?

Answer 1

For this problem, we will use the following `ln` properties:

`• ln^a = aln`
`• ln(x/y) = lnx - lny`
`• ln(xy) = lnx + lny`

First, let's establish that `sqrt(a) = a^(1/2)`

Therefore, `ln(sqrt((xy^2)/z)) = ln((xy^2)/z)^(1/2)`

`= 1/2ln((xy^2)/z)`

`= 1/2(lnxy^2 - lnz)`

`= 1/2(lnx + lny^2 - lnz)`

Hopefully this helps!