Question

Solve the following inequality:
${\log }_{1/3}(3x+4)>{\log }_{1/3}(x^2+2)$

Answer 1

$-\log (3x+4)>-{\log }_3(x^2+2)$

${\log }_3(3x+4)<{\log }_3(x^2+2)$

$3x+4<x^2+2$

$x^2-3x-2>0$

${(x-\frac{3}{2})}^2-\frac{17}{4}>0$

$x\epsilon (-\infty ,\frac{3-\sqrt{17}}{2})\bigcup (\frac{3+\sqrt{17}}{2},\infty )$