Question

Find the domain of definition of the following function:
$y={\log }_{100x}\frac{2\log x+2}{-x}.$

Answer 1

$x>0$

$\frac{2logx+2}{-x}>0$

$2logx+2<0$ as $x>0$ it is not possible fo $x>1$

for $x\in (0,1)$ $logx<0$

$2logx<-2$

$x<e^{-1}$

$x\in (0,e^{-1})$