Question

How do you expand `ln (sqrt(ex^2)/y^3)`?

Answer 1

`1/2+lnx-3lny`

Explanation:

Expanding this expression is done by applying two properties of `ln`
Quotient property:
`ln (a/b)=lna-lnb`

Product property:
`ln (a*b)=lna+lnb`

`Ln ((sqrt (ex^2))/y^3)`
`=ln (sqrt (ex^2 ))-ln (y^3)`
`=ln((ex^2)^(1/2))-3lny`
`=1/2ln (ex^2)-3lny`
`=1/2 (lne+ln (x^2))-3lny`
`=1/2 (1+2lnx)-3lny`
`=1/2+lnx-3lny`