Question

Solve the following inequality:
${\log }_{0.5}\sqrt{\frac{x-4}{x-3}}<{\log }_{0.5}2$

Answer 1

$-{\log }_2\sqrt{\frac{x-4}{x-3}}<-{\log }_{2}2$

${\log }_2\sqrt{\frac{x-4}{x-3}}>{\log }_{2}2$

$\sqrt{\frac{x-4}{x-3}}>2$

$\frac{x-4}{x-3}>4$

$\frac{x-4-4x+12}{x-3}>0$

$\frac{-3x+8}{x-3}>0$

$\frac{3x-8}{x-3}<0$

$x\epsilon (\frac{8}{3},3)$