solve for the variable?

3e^(2x - 2) - 3 = 9

we want to get the "e" term by itself, so start with adding 3 to both sides:

3e^(2x - 2) = 12

Then divide 3 from both sides:

e^(2x - 2) = 4

Now get the natural log of both sides to cancel out the "e":

2x - 2 = ln(4)

and finish:

2x = 2 + ln(4)
x = 1 + ln(4)/2