Symbiosis National Aptitude Test SNAP 2016 Paper

u = ${\left({\log }_2\mathit{x}\right)}^2\mathit{–}6{\log }^2\mathit{x}+12$
⇒ xu = 256
Let ${\log }_2\mathit{x}$ = y
⇒ x = 2y
${\mathit{x}}^{\mathit{u}}$ = 28
⇒ uy = 8
⇒ u = 8/y
⇒ ∴ 8/y = ${\mathit{y}}^2$ – 6y + 12
⇒ ${\mathit{y}}^3\mathit{–}6{\mathit{y}}^2$ + 12y – 8 = 0
⇒ ${\left(\mathit{y}\mathit{–}2\right)}^3$ = 0
⇒ y = 2
∴ x = 4, u = 4