Помогите решить неравенства. Заранее спасибо. [latex]3 ^{x} - 3 ^{x-3} \ \textgreater \ 26 2 ^{x+2} + 2 ^{x+5} \ \textless \ 9[/latex]

Ну по-моему можно так: [latex]3^x-3^{x-3}\ \textgreater \ 26[/latex] [latex]3^x(1-3^{-3})=3^x(1- \frac{1}{3^3} )=3^x(1- \frac{1}{27} )=3^x(\frac{26}{27} )\ \textgreater \ 26[/latex] [latex] 3^x\ \textgreater \ 26* \frac{27}{26}=27[/latex] [latex] 3^x\ \textgreater \ 27 [/latex] Теперь логарифмируем обе части [latex]x\ \textgreater \ log_{3}(27) [/latex] [latex]x\ \textgreater 3[/latex] [latex] 2^{x+2}+2^{x+5}\ \textless \ 9[/latex] [latex] 2^x(2^{2}+2^{5})=2^x(4+32)=2^x*36\ \textless \ 9[/latex] [latex] 2^x*36\ \textless \ 9[/latex] [latex] 2^x\ \textless \ 9/36=1/4[/latex] [latex] 2^x\ \textless \ 1/4 [/latex] [latex] log_{2}(2^x)\ \textless \ log_{2}(1/4)[/latex] [latex] x\ \textless \ log_{2}(2^{-2})=-2[/latex] [latex]x\ \textless -2[/latex]