Few more Algebra problems..

I have a couples problems with certain types of problems. I cant seem how to figure these ones out, any help is appreciated.

1. Find x and express answer in terms of natural logarithms: 2e^3x=6

2. Express 1+ ln as a single logarithm.

3. Write log(x+3) in terms of natural logarithms.

4. Solve with Gauss Jordan method (I can get half way done but I never seem to be able to finish the whole problem.)

x-y-3z=2

2x-y-4z=3

x+y-z=1

5. How to Maximize Z=2x-3y subject to

2x+y>=1

x-y=<1

x,y>=0

6. Similar can probably figure it with some help from previous one.

Maximize Z=2x-3y subject to

-x+y=<2

3x+y=<18

x,y>=0

All help appreciated.