Question

Решите неравенство $3^{x-3} +\frac{3^{x}}{3}\ \textless \ 10$

Answer 1

$3^{x-3}+ \frac{3^x}{3}-10\ \textless \ 0 \\ \\ 3^x*3^{-3}+ \frac{3^x}{3}-10\ \textless \ 0 \\ \\ \frac{3^x}{27}+ \frac{3^x}{3}-10\ \textless \ 0 \ (*27) \\ \\ 3^x+ 9*3^x-270\ \textless \ 0 \\ 3^x(1+9)\ \textless \ 270 \\ 3^x*10\ \textless \ 270 \\ 3^x\ \textless \ 27 \\ 3^x\ \textless \ 3^3 \\ x\ \textless \ 3 \\ \\ x \in (-\infty;3)$