I need to solve for x and have no clue what I'm doing

Please clarify- do you mean:


2^x - 2^{(\frac {-x}{3})} = 4

or:


2^x - \frac {2^{(-x)}} 3 = 4


?

Solving the first involves solving a 4th order polynomial: let u = 2^{x/3} and you get u^4-4u-1 = 0. Solve for u, then

x = 3 \frac {\ln(u)}{\ln(2)}

Solving the second is easier. Let u = 2^x, which leads to u^2-4u - 1/3 = 0, which can be solved with the quadratic formula. Then x = \frac { \ln(u)}{ \ln(2)}