Question

Solve the following inequality:
${\log }_{0.5}^{2}x+{\log }_{0.5}x-2⩽0$

Answer 1

${\log }_{0.5}x=-{\log }_{2}x$

$let{\log }_{2}x=z$

$+z^2-z-2\le 0$

$(z-2)(z+1)\le 0$

$z\epsilon [-1,2]$

$-1\le z\le 2$

$-1\le {\log }_{2}x\le 2$

taking antilog,we get

$\frac{1}{2}\le x\le 4$