Question

ПОЖАЛУЙСТА
Решите неравенство:

$3*9^{x} -2*15^{x} -5^{2x+1} \ \textgreater \ 0$

Answer 1

$\mathtt{3*9^x-2*15^x-5^{2x+1}\ \textgreater \ 0;~\frac{3*9^x-2*15^x-25^x*5}{25^x}\ \textgreater \ \frac{0}{25^x};~}\\\\\mathtt{3*\frac{9^x}{25^x}-2*\frac{15^x}{25^x}-5=3(\frac{3}{5})^{2x}-2(\frac{3}{5})^x-5=3[(\frac{3}{5})^x+1][(\frac{3}{5})^x-\frac{5}{3}]\ \textgreater \ 0,~}\\\\\mathtt{\to(\frac{3}{5})^x\ \textgreater \ \frac{5}{3}=(\frac{3}{5})^{-1},~\to~x\ \textless \ -1}$