1) 3^(2x-4) = 1/9
Rewrite 1/9 as 3^(-2)
3^(2x-4) = 3^(-2)
2x-4 = -2
2x = 2
x = 1

2) 4^(-x) 4^(2x+3) = 1/4
Rewrite 1/4 as 4^(-1)
4^(-x) 4^(2x+3) = 4^(-1)
Using the properties of exponents, we can combine the terms on the left side:
4^(2x+3-x) = 4^(-1)
4^(x+3) = 4^(-1)

Since the bases are the same, we can equate the exponents:
x+3 = -1
x = -4

Therefore, the solutions are x = 1 and x = -4.