Question

Solve the following inequalities.
$lo{g}_{0.5}\left(\right(2-x\left)/3\right)<0.$

Answer 1

${\log }_{0.5}\left(\right(2-x\left)/3\right)<0$

$⟹\frac{2-x}{3}>1$

$⟹2-x>3$

$⟹x<-1$

And for $\log$ to be defined-

$2-x>0⟹x<2$

Hence the solution is $x\in (-\infty ,-1)$