for xlnx-x=0 take out an x so : x(lnx-1)=0 so by this the roots are x=0 and x=e

lne=1 by the way; they are inverses

for 1. use the muliplication/addition rule for natural logs so that becomes :ln((2x-1)(3x-2))=ln7 and raise them both to the power of e so you get (2x-1)(3x-2)=7. I think you can take it from here.

for 2, use the division/subtraction rule for natural logs. clue: ln ((x-1)/(x-3))=1. repeat steps from above

for 3: x^2*2e^x=e^x*(1-x) (subtract e^x on other side and factor it out) then you can divide both sides by e^x so you have 2x^2=(1-x). You can solve from here

P.S. it looks like your trying to get us to do your whole homework for you. Instead of waiting for an answer try to finish the work yourself. Just getting an answer is not enough. Understanding the material itself is what is important. Sometimes you run into holes and can't figure it out. Spend an hour or so and if your having trouble, ask a few questions. This seems a little ridiculous