Question

How do you expand `ln(x/y) - 2ln(x^3) -4lny`?

Answer 1

Answer:
after expanding `-5lnx-5lny`
after simplication `-ln(xy)^5`

Explanation:

`ln(A/B) = ln A - ln B`
`ln(AB) = lnA+lnB`
`ln(A^B) = B*lnA`

Using the above two rules we can expand the given expression into:

`lnx - lny -2*3*lnx-4lny`
`rArrlnx-lny-6lnx-4lny`
`or, -5lnx-5lny`

On further simplification we get

`-5(lnx +lny)`
`or-5*lnxy`
`or-ln(xy)^5`