Attached are a few questions I have about operations concerning ln and ln e.

Any help would be greatly appreciated.

1.

The book has:

lne^(-2x)=e^(-2x)

I thought lne^(-2x)=-2x

2.

3e^(ln8/3)=3e^(ln2) How does Ln8/3=ln2?

3.1/2(ln27-ln3)=Ln3

How do we get ln3 as an answer.