Question

Решить неравенство
$( \frac{1}{9} )^{-5x/2 } \ \textgreater \ 27$

Answer 1

$\Big(\dfrac{1}{9}\Big)^{-\dfrac{5x}{2} }>27\\\\\Big[\Big(3^{-2} \Big)\Big]^{-\dfrac{5x}{2} } >3^{2}\\\\3^{5x}>3^{2}\\\\3>1 \ \Rightarrow \ 5x>2\\\\x>0,4\\\\Otvet:\boxed{x\in(0,4 \ ; \ +\infty)}$