The limit `lim_(x->0) (2^(2x) + 2*2^x - 3)/(2^x - 1)` has to be determined.

`lim_(x->0) (2^(2x) + 2*2^x - 3)/(2^x - 1)`

`= lim_(x->0) (2^(2x) + 3*2^x - 2^x - 3)/(2^x - 1)`

`= lim_(x->0) (2^x(2^x + 3) - 1(2^x + 3))/(2^x - 1)`

`= lim_(x->0) ((2^x - 1)(2^x + 3))/(2^x - 1)`

`= lim_(x->0) (2^x + 3)`

Substitute x = 0

=> 1 + 3 = 4

**The limit `lim_(x->0) (2^(2x) + 2*2^x - 3)/(2^x - 1) = 4` **

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