Question

What is the solution to log^2 (2x^3 -8)-2log ^2 x= log^2x

Answer 1

Hey


`log_(2)(2 {x}^(3) - 8) - 2 log_(2)(x) = log_(2)(x)`

Transposing log x to other side :


`= > log_(2)(2 {x}^(3) - 8) = log_(2)(x) + 2 log_(2)(x)`
Using Logarithmic Property :


`= > log_(2)(2 {x}^(3) - 8) = log_(2)( {x}^(3) )`

Raising to the power 2 :


`{x}^(3) - 8 = 0`


`= > (x - 2)( {x}^(2) + 2x + 4) = 0`


`= > x = 2`

Hence, [ x = 2 ] is the only real solution !