Question

Solve the following inequality:
$(0.2{)}^{\frac{2x-3}{x-2}}>5$

Answer 1

${\left(\frac{2}{10}\right)}^{\frac{2x-3}{x-2}}>{\left(5\right)}^1$

${\left(\frac{1}{5}\right)}^{\frac{2x-3}{x-2}}>5^1$

${\left(5\right)}^{\frac{2x-3}{2-x}}>5^1$

$\frac{2x-3}{2-x}-1>0$

$\frac{2x-3-2+x}{2-x}>0$

$\frac{3x-5}{x-2}<0$

$\frac{x-\frac{5}{3}}{x-2}<0$

$x\epsilon (\frac{5}{3},2)$