Respuesta :

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 !

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