Question

Solve the following inequalities.
$log\left(6/x\right)>log(x+5).$

Answer 1

$\log \left(6/x\right)>\log (x+5)$

For $\log$ to be defined-

$\frac{6}{x}>0$ and $x+5>0$

$⟹x>0$

Now , coming to inequality-

$\frac{6}{x}>x+5$

$⟹x^2+5x-6<0$

$⟹(x+6)(x-1)<0$

$⟹x\in (-6,1)$

Hence overall solution is-

$x\in (0,1)$