We have to solve for x: 2^( x^2 - 3x + 2) = 4^3

2^( x^2 - 3x + 2) = 4^3

=> 2^( x^2 - 3x + 2) = 2^2^3 = 2^6

as the base 2 is equal we equate the exponent.

x^2 - 3x + 2 = 6

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We have to solve for x: 2^( x^2 - 3x + 2) = 4^3

2^( x^2 - 3x + 2) = 4^3

=> 2^( x^2 - 3x + 2) = 2^2^3 = 2^6

as the base 2 is equal we equate the exponent.

x^2 - 3x + 2 = 6

=> x^2 - 3x -4 = 0

=> x^2 - 4x + x - 4 = 0

=> x(x - 4) +1(x - 4) = 0

=> (x + 1)(x - 4) = 0

**=> x = -1 and x = 4**