0\\\dfrac{(x-2)^7}{x-1}>0\end{array}\right\ \ \left\{\begin{array}{l}(x-1)(x-1)>0\\\dfrac{(x-2)^7}{x-1}>0\end{array}\right\ \ \Rigyhtarrow \ \ x\in (-\infty ;\, 1\, )\cup (2;+\infty )\\\\\\log_9(x-2)^2(x-1)^7-log_99^8-log_9\dfrac{(x-2)^7}{x-1}\leq 0\ \ ,\ \ \ 0=log_91\ ,\\\\\\\dfrac{(x-2)^7(x-1)^7(x-1)}{9^8\cdot (x-2)^7}\leq 1\ \ ,\ \ \dfrac{(x-1)^8}{9^8}-1\leq 0\ \ ,\ \dfrac{(x-1)^8-9^8}{9^8}\leq 0\ ," alt="7\cdot log_9(x^2-3x+2)\leq 8+log_9\dfrac{(x-2)^7}{x-1}\ \ ,\\\\\\ODZ:\ \left\{\begin{array}{l}x^2-3x+2>0\\\dfrac{(x-2)^7}{x-1}>0\end{array}\right\ \ \left\{\begin{array}{l}(x-1)(x-1)>0\\\dfrac{(x-2)^7}{x-1}>0\end{array}\right\ \ \Rigyhtarrow \ \ x\in (-\infty ;\, 1\, )\cup (2;+\infty )\\\\\\log_9(x-2)^2(x-1)^7-log_99^8-log_9\dfrac{(x-2)^7}{x-1}\leq 0\ \ ,\ \ \ 0=log_91\ ,\\\\\\\dfrac{(x-2)^7(x-1)^7(x-1)}{9^8\cdot (x-2)^7}\leq 1\ \ ,\ \ \dfrac{(x-1)^8}{9^8}-1\leq 0\ \ ,\ \dfrac{(x-1)^8-9^8}{9^8}\leq 0\ ," align="absmiddle" class="latex-formula">
![\star \ \ \ a^8-b^8=(a^4-b^4)(a^4+b^4)=(a-b)(a+b)(\underbrace {a^2+b^2}_{\geq 0})(\underbrace {a^4+b^4}_{\geq 0})\ \ \star \\\\\\(x-1-9)(x-1+9)\leq 0\\\\(x-10)(x+8)\leq 0\ \ \ ,\ \ \ \ +++[-8\, ]---[\, 10\, ]+++\\\\x\in [-8\, ;\, 10\, ]\\\\\\\left\{\begin{array}{l}x\in (-\infty ;1)\cup (2;+\infty )\\x\in [-8\, ;\, 10\, ]\end{array}\right\qquad \Rightarrow \quad x\in [-8\, ;1\, )\cup (\, 2\, ;10\, ]](https://tex.z-dn.net/?f=%5Cstar%20%5C%20%5C%20%5C%20a%5E8-b%5E8%3D%28a%5E4-b%5E4%29%28a%5E4%2Bb%5E4%29%3D%28a-b%29%28a%2Bb%29%28%5Cunderbrace%20%7Ba%5E2%2Bb%5E2%7D_%7B%5Cgeq%200%7D%29%28%5Cunderbrace%20%7Ba%5E4%2Bb%5E4%7D_%7B%5Cgeq%200%7D%29%5C%20%5C%20%5Cstar%20%5C%5C%5C%5C%5C%5C%28x-1-9%29%28x-1%2B9%29%5Cleq%200%5C%5C%5C%5C%28x-10%29%28x%2B8%29%5Cleq%200%5C%20%5C%20%5C%20%2C%5C%20%5C%20%5C%20%5C%20%2B%2B%2B%5B-8%5C%2C%20%5D---%5B%5C%2C%2010%5C%2C%20%5D%2B%2B%2B%5C%5C%5C%5Cx%5Cin%20%5B-8%5C%2C%20%3B%5C%2C%2010%5C%2C%20%5D%5C%5C%5C%5C%5C%5C%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bl%7Dx%5Cin%20%28-%5Cinfty%20%3B1%29%5Ccup%20%282%3B%2B%5Cinfty%20%29%5C%5Cx%5Cin%20%5B-8%5C%2C%20%3B%5C%2C%2010%5C%2C%20%5D%5Cend%7Barray%7D%5Cright%5Cqquad%20%5CRightarrow%20%5Cquad%20x%5Cin%20%5B-8%5C%2C%20%3B1%5C%2C%20%29%5Ccup%20%28%5C%2C%202%5C%2C%20%3B10%5C%2C%20%5D "\star \ \ \ a^8-b^8=(a^4-b^4)(a^4+b^4)=(a-b)(a+b)(\underbrace {a^2+b^2}_{\geq 0})(\underbrace {a^4+b^4}_{\geq 0})\ \ \star \\\\\\(x-1-9)(x-1+9)\leq 0\\\\(x-10)(x+8)\leq 0\ \ \ ,\ \ \ \ +++[-8\, ]---[\, 10\, ]+++\\\\x\in [-8\, ;\, 10\, ]\\\\\\\left\{\begin{array}{l}x\in (-\infty ;1)\cup (2;+\infty )\\x\in [-8\, ;\, 10\, ]\end{array}\right\qquad \Rightarrow \quad x\in [-8\, ;1\, )\cup (\, 2\, ;10\, ]")