Hey
[tex] log_{2}(2 {x}^{3} - 8) - 2 log_{2}(x) = log_{2}(x) [/tex]
Transposing log x to other side :
[tex] = > log_{2}(2 {x}^{3} - 8) = log_{2}(x) + 2 log_{2}(x) [/tex]
Using Logarithmic Property :
[tex] = > log_{2}(2 {x}^{3} - 8) = log_{2}( {x}^{3} ) [/tex]
Raising to the power 2 :
[tex] {x}^{3} - 8 = 0[/tex]
[tex] = > (x - 2)( {x}^{2} + 2x + 4) = 0[/tex]
[tex] = > x = 2[/tex]
Hence, [ x = 2 ] is the only real solution !
