Question

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

Answer 1

${\log }_{1/2}x+{\log }_{3}x>1x>0$

$\frac{\log x}{\log \left(1/2\right)}+\frac{\log x}{\log 3}>1xϵ(0,\infty )$

$\log x[-\frac{1}{\log 2}+\frac{1}{\log 3}]>1$

$-\log x\left[\frac{\log 3-\log 2}{\log 2\log 3}\right]>1$

$\log x<-\left[\frac{\log 2\log 3}{\log 3/2}\right]$

$x<0.152xϵ(-\infty ,0.152)$

Taking intersection we get

$xϵ(0,0.152)$