Решите неравенства: 3^(2x-5)+3^(2x-6)-3^(2x-7)-3^(2x-8)≤32 5^4x-5^(4x-1)+5^(4x-2)-5^(4x-3)≥104

[latex]1)[/latex] [latex] 3^{2x-5} + 3^{2x-6} - 3^{2x-7} - 3^{2x-8} \leq 32[/latex] [latex] 3^{2x-5}(1+ 3^{-1} - 3^{-2} - 3^{-3}) \leq 32[/latex] [latex] 3^{2x-5}(1+\frac{1}{3} } - \frac{1}{9} - \frac{1}{27} ) \leq 32[/latex] [latex] 3^{2x-5}(1+ \frac{9}{27} } - \frac{3}{27} - \frac{1}{27} ) \leq 32[/latex] [latex] 3^{2x-5}*1 \frac{5}{27} } \leq 32[/latex] [latex] 3^{2x-5}*\frac{32}{27} } \leq 32[/latex] [latex] 3^{2x-5} \leq 32* \frac{27}{32} [/latex] [latex]3^{2x-5} \leq 27[/latex] [latex]3^{2x-5} \leq 3^3[/latex] [latex]2x-5 \leq 3[/latex] [latex]2x \leq 8[/latex] [latex]x \leq 4[/latex] -------------[4]----------- ////////////// Ответ: [latex](-[/latex] ∞ [latex];4][/latex] [latex]2)[/latex] [latex] 5^{4x} - 5^{4x-1} + 5^{4x-2} - 5^{4x-3} \geq 104[/latex] [latex] 5^{4x} (1- 5^{-1} + 5^{-2} - 5^{-3}) \geq 104[/latex] [latex]5^{4x} (1- \frac{1}{5} + \frac{1}{25} - \frac{1}{125} ) \geq 104[/latex] [latex]5^{4x} (1- \frac{25}{125} + \frac{5}{125} - \frac{1}{125} ) \geq 104[/latex] [latex]5^{4x} * \frac{104}{125} \geq 104[/latex] [latex]5^{4x} \geq 104* \frac{125}{104} [/latex] [latex]5^{4x} \geq 125[/latex] [latex]5^{4x} \geq 5^3[/latex] [latex]4x \geq 3[/latex] [latex]x \geq 0.75[/latex] ----------[0.75]-------------                  ///////////////// Ответ:  [latex][0.75;+[/latex] ∞ [latex])[/latex]