Solve Logarithms symbolically

Ok, this is my first post so here goes.

I am trying to solve

*Use common or natural logarithms to solve symbolically.*

2e^2x+2= 6

first I divide both sides by 2

e^2x+2= 6

use natural logarithms

ln e^2x+2 = ln 6

Simplify

2x+2 = ln 6

subtract 2 from both sides

2x = ln 6-4

Divide by 2

x = ln 6-4/2

I enter this into my Ti-83plus

ln (6-4)/2

my answer is .34657 It is wrong I figure it is the way I have entered it into the calc. Anybody have any thoughts of what is wrong?

symbolically answer exponential equation

Thank you for the pointers, still not getting the right answer

e^2x+1 = 3

ln e^2x+1 = ln 3

2x+1 = ln 3

2x = ln 3-1

x = ln 3-1/2

.34657

still not the right answer. I am doing something else wrong?