Question

Помогите решить неравенства. Заранее спасибо.

Answer 1

$1)~3^x-3^{x-3}\ \textgreater \ 26 \\ \\ ~~~~3^x- \frac{3^x}{3^3} \ \textgreater \ 26 \\ \\ ~~~~3^x- \frac{3^x}{27} \ \textgreater \ 26 ~|*27\\ \\ ~~~~27*3^x-3^x\ \textgreater \ 702 \\ ~~~~26*3^x\ \textgreater \ 702 \\ ~~~~3^x\ \textgreater \ 27 \\ ~~~~3^x\ \textgreater \ 3^3 \\ ~~~~x\ \textgreater \ 3$
Ответ: $x$ ∈ $(3;+$ беск.$)$

$2)~2^{x+2}+2^{x+5}\ \textless \ 9 \\ ~~~~2^x*2^2+2^x*2^5\ \textless \ 9 \\ ~~~~2^x*4+2^x*32\ \textless \ 9 \\ ~~~~2^x(4+32)\ \textless \ 9 \\ ~~~~2^x*36\ \textless \ 9 \\ ~~~~ 2^x\ \textless \ ~\frac{9}{36} \\ ~~~~2^x\ \textless \ \frac{1}{4} \\ ~~~~2^x\ \textless \ 2^{-2} \\ ~~~~x\ \textless \ -2$
Ответ: $x$ ∈ $(-$ беск.$;-2)$