Question

Solve the following inequalities.
$lo{g}_{1/2}(x+4)<2.$

Answer 1

${\log }_{1/2}(x+4)<2$

$x+4>0⟹x>-4$ for $\log$ to be defined

$⟹x+4>{\left(\frac{1}{2}\right)}^2$

$⟹4(x+4)>1$

$⟹x>\frac{-15}{4}$

Hence, the final solution is

$x>\frac{-15}{4}$ that is $x\in (\frac{-15}{4},\infty ]$