Exponential equation (find x)

Take log of both sides to get

(3-x) LOG 2 = (2x+3) LOG (1/3)      LOG2 =.3010    LOG(1/3) = -.4771

.90308 - .301x = -.9542x - 1.4313     Now just solve for 'x'

2.33438= -.6532x

x= -3.5738

Solve for x over the real numbers:
2^(3 - x) = 3^(-3 - 2 x)

Take reciporicals of both sides:
2^(x - 3) = 3^(2 x + 3)

Take the natural logarithm of both sides and use the identity log(a^b) = b log(a):
log(2) (x - 3) = log(3) (2 x + 3)

Expand out terms of the left hand side:
log(2) x - 3 log(2) = log(3) (2 x + 3)

Expand out terms of the right hand side:
log(2) x - 3 log(2) = 2 log(3) x + 3 log(3)

Subtract 2 x log(3) - 3 log(2) from both sides:
(log(2) - 2 log(3)) x = 3 log(2) + 3 log(3)

Divide both sides by log(2) - 2 log(3):
Answer: |x = (3 log(2) + 3 log(3))/(log(2) - 2 log(3))= -3.573804392782666.........