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Solution

log2(x-4) +log2(x+3) =3

log2(x-4)(x+3) =3

(x-4)(x+3) = 8

x^2 -x - 20 =0

x^2 - 5x +4x -20 =0

(x-5)(x+4) =0

x = -4 , 5

Neglect x =-4 as log2(x+3) = 2log2(-1)

So, solution x =5