2^(x^2)=4^(3x-4) find x?

4^(3x-4) is the same as

2^(2(3x-4)

so then you have

x^2 = 2(3x-4)

x^2 = 6x - 8

x^2 - 6x +8 = 0

(x - 2)(x - 4)

x = 2, 4

2^(x^2) = 4^(3x - 4)
2^(x^2) = (2^2)^(3x - 4)
2^(x^2) = 2^[2(3x - 4)]
x^2 = 2(3x - 4)
x^2 = 2(3x) - 2(4)
x^2 = 6x - 8
x^2 - 6x + 8 = 0
x^2 - 2x - 4x + 8 = 0
(x^2 - 2x) - (4x - 8) = 0
x(x - 2) - 4(x - 2) = 0
(x - 2)(x - 4) = 0

x - 2 = 0
x = 2

x - 4 = 0
x = 4

∴ x = 2, 4

2^(x^2)=2^2(3x-4)
x^2=6x-8
x^2-6x+8=0
(x-4)(x-2)=0
x=2
&
x=4
God bless you.