1. Do you mean solve for t? If so, take the natural log of both sides and continue from there.

2. Absolute value gets rid of negative signs, so with the equation you need to solve, the 2x+3 part can be either positive or negative, and it won't matter to the rest of the equation. Hence, you split up the whole thing into two equations:
2x+3=+(2-x)
2x+3=-(2-x)
It can be a little difficult to 'see' right away, but it's there

3. Use integration by parts. There are many sites and books that give explain this method.