We need to solve (log(2) x)^2 + log(2) (4x) = 4

Use the property that log a*b = log a + log b

(log(2) x)^2 + log(2) (4x) = 4

=> (log(2) x)^2 + log(2) 4 + log(2) x = 4

=> (log(2) x)^2 + 2 + log(2) x = 4

=> (log(2) x)^2 + log(2) x = 2

Let log(2)x = y

=> y^2 + y - 2 = 0

=> y^2 + 2y - y - 2 = 0

=> y(y + 2) - 1(y + 2) = 0

=> (y - 1)(y + 2) = 0

=> y = 1 and y = -2

log(2) x = 1 => x = 2

log(2) x = -2 => x = 1/4

**The solutions for x are 2 and 1/4**

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