Questions about natural log

thatguy47

Junior Member
Joined
Aug 11, 2008
Messages
69
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.
 
ln(32)=ln(3)ln(2)\displaystyle \ln \left( {\frac{3}{2}} \right) = \ln (3) - \ln (2)
3ln(3)5ln(2)=?\displaystyle 3\ln (3) - 5\ln (2) = ?
 
3ln(3/2)2ln2\displaystyle 3\ln(3/2) - 2\ln2
ln(3/2)3ln22\displaystyle \ln(3/2)^3 - \ln2^2
ln(27/8)ln4\displaystyle \ln(27/8) - \ln4
ln27/84\displaystyle \ln\frac{27/8}{4}
 
Top