Question

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

Answer 1

$-{\log }_2(3x-4)<-{\log }_2(x-2)$

${\log }_2(3x-4)>{\log }_2(x-2)$

$3x-4>x-2$

$2x>2$

$x>1$

$and3x-4>0andx>2$

$x>\frac{4}{3}andx>2$

$therefore,x\epsilon (2,\infty )$