Ответ:
Объяснение:
0 ;x<7\\7-x\leq 0,6^{2} \\7-x\leq 0,36\\x\geq 6,64\\" alt="A)\\logx_{0,6} (7-x)\geq 2 ;\\ODZ:7-x>0 ;x<7\\7-x\leq 0,6^{2} \\7-x\leq 0,36\\x\geq 6,64\\" align="absmiddle" class="latex-formula">
Ответ: x∈[6,64;7).
Б)
0; x>-0,86\\x+0,86\leq 7^{1} \\x+0,86\leq 7\\x\leq 6,14." alt="log_{7} (x+0,86)\leq 1\\ODZ:x+0,86>0; x>-0,86\\x+0,86\leq 7^{1} \\x+0,86\leq 7\\x\leq 6,14." align="absmiddle" class="latex-formula">
Ответ: х∈(-0,86;6,14]
B)
![(\frac{1}{4} )^{x^{2}+2x } \geq \frac{1}{64} \\\geq (\frac{1}{4} )^{x^{2}+2x } \geq (\frac{1}{4})^{3} \\x^{2}+2x\leq 3\\x^{2} +2x-3\leq 0\\D=16;\sqrt{D}=4\\x_{1} =-3;x_{2} =1. (\frac{1}{4} )^{x^{2}+2x } \geq \frac{1}{64} \\\geq (\frac{1}{4} )^{x^{2}+2x } \geq (\frac{1}{4})^{3} \\x^{2}+2x\leq 3\\x^{2} +2x-3\leq 0\\D=16;\sqrt{D}=4\\x_{1} =-3;x_{2} =1.](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B4%7D%20%29%5E%7Bx%5E%7B2%7D%2B2x%20%7D%20%5Cgeq%20%5Cfrac%7B1%7D%7B64%7D%20%5C%5C%5Cgeq%20%28%5Cfrac%7B1%7D%7B4%7D%20%29%5E%7Bx%5E%7B2%7D%2B2x%20%7D%20%5Cgeq%20%28%5Cfrac%7B1%7D%7B4%7D%29%5E%7B3%7D%20%20%5C%5Cx%5E%7B2%7D%2B2x%5Cleq%203%5C%5Cx%5E%7B2%7D%20%2B2x-3%5Cleq%200%5C%5CD%3D16%3B%5Csqrt%7BD%7D%3D4%5C%5Cx_%7B1%7D%20%3D-3%3Bx_%7B2%7D%20%3D1.)
Г)
![5^{(2x-7)(x+1)} <1\\5^{(2x-7)(x+1)} <5^{0} \\(2x-7)(x+1)<0 5^{(2x-7)(x+1)} <1\\5^{(2x-7)(x+1)} <5^{0} \\(2x-7)(x+1)<0](https://tex.z-dn.net/?f=5%5E%7B%282x-7%29%28x%2B1%29%7D%20%3C1%5C%5C5%5E%7B%282x-7%29%28x%2B1%29%7D%20%3C5%5E%7B0%7D%20%5C%5C%282x-7%29%28x%2B1%29%3C0)
-∞__+__-1__-__3,5__+__+∞
x∈(-1;3,5).
Д)
0;\\(x-8)(6-x)\geq 0\\" alt="\frac{(x-8)(6-x)}{(2-x)^{2} }\geq 0\\ODZ:(2-x)^{2} \neq 0;2-x\neq 0;x\neq 2\\(2-x)^{2} >0;\\(x-8)(6-x)\geq 0\\" align="absmiddle" class="latex-formula">
-∞_-_(2)_-_6__+__8__-__+∞
x∈[6;8].