Question

Number of values of x satisfying the equation x⁴=|x|^log2(x²+2)?​

Answer 1

Step-by-step explanation:

We have,

${x}^{4} = |x|^{ log_{2}( {x}^{2} + 2 ) }$

$= > log_{x}( {x}^{4} ) = log_{x}( |x|^{ log_{2}( {x}^{2} + 2) } )$

$= > 4 = log_{2}( {x}^{2} + 2 )$

$= > {x}^{2} + 2 = {2}^{4}$

$= > {x}^{2} = 16 - 2$

$= > x = + - \sqrt{14}$