[tex] log_{2} x + log_{2} (x-7) = 3[/tex]
[tex] log_{2} (x)(x-7) = 3[/tex]
[tex] 2^{ log_{2} (x)(x-7)} = 2^{3}[/tex]
[tex]x(x-7) = 8[/tex]
[tex]x^{2} - 7x -8 = 0[/tex]
[tex] \left \{ {{ x_{1} = 8} \atop { x_{2} =-1}} \right. [/tex]
Since in [tex] log_{a} x[/tex] x>0, then the answer is x=8 only.
Hope it helps!
