Use the Laws of Logarithms to expand the expression?

Question

1.) ln cubert3(sqrt 3r^2s))

Answer 1

are you asking

ln(cbrt(sqrt(3r^2s))) =
ln((3r^2s)^(1/2))^(1/3) =
ln((3r^2s)^(1/6)) =
(1/6)ln(3r^2s) =
(1/6)(ln(3) + ln(r^2) + ln(s)) =
(1/6)(ln(3) + 2ln(r) + ln(s))