how do i do this logrithm equation>? :(?

Question

ln(r^9s^3 √r^9s^7)

^ = raised to power.
√ = Square root of all terms that follow this sign

Answer 1

ln{r^9 s^3 √(r^9s^7)} = ln{r^[9 + (9/2)]s^[3 + (7/2)]}
= ln{r^(27/2) s^(13/2)} = ln{r^(27/2)} + ln{s^(13/2)}
= (27/2)(ln r) + (13/2)(ln s)

Answer 2

Simplify.

ln{r^9 * s^3 * r^9/2 * s^7/2}

ln{r^27/2 * s^13/2} = ln{r^27/2} + ln{ s^13/2}

trivial after that...