2-(1/7)ln(6)+(1/7)ln(4/3) is not 2-(1/7)ln(8).
because it is equal to your answer if it is written as
2-[(1/7)ln(6)+(1/7)ln(4/3)]
I am trying to figure out why 2-(1/7)ln(6)+(1/7)ln(4/3) is not 2-(1/7)ln(8). I know if you rearrange it as 2+(1/7)ln(4/3)-(1/7)ln(6) you get 2+(1/7)ln(2/9) which is the correct answer...which is using the lnx-lny=ln(x/y) rule. However how come you cannot apply the lnx+lny=ln(xy) rule for 2-(1/7)ln(6)+(1/7)ln(4/3).
thanks