Questions about natural log

[thatguy47]

After solving a problem I got 3ln(3/2) - 2ln2
On the answer key it says the answer is ln(27/32)
When I solve both on the calculator they equal each other. Is my answer(the 1st one) not simplified? How would you simplify it (steps to get from "3ln(3/2) - 2ln2" to "ln(27/32)"

Thanks for the help.

 

[pka]

\(\displaystyle \ln \left( {\frac{3}{2}} \right) = \ln (3) - \ln (2)\)
\(\displaystyle 3\ln (3) - 5\ln (2) = ?\)

 

[Loren]

\(\displaystyle 3\ln(3/2) - 2\ln2\)
\(\displaystyle \ln(3/2)^3 - \ln2^2\)
\(\displaystyle \ln(27/8) - \ln4\)
\(\displaystyle \ln\frac{27/8}{4}\)

 

[thatguy47]

Thanks, that makes sense.