укажите все натуральные решения неравенства
log1/3(x^2-6x+8) ≥ -1
x^2-6*x+8<=3</p>
{
x^2-6*x+8>0;
x=[1;5]
x=(-беск;2)U(4;беск);
x=1;5
ОДЗ:
0\\(x-2)(x-4)>0\\x\in (-\infty;2)\cup(4;+\infty)" alt="x^2-6x+8>0\\(x-2)(x-4)>0\\x\in (-\infty;2)\cup(4;+\infty)" align="absmiddle" class="latex-formula">
Целые решения: 1 ; 5
0\\(x-2)(x-4)>0\\x\in (-\infty;2)\cup(4;+\infty)" alt="x^2-6x+8>0\\(x-2)(x-4)>0\\x\in (-\infty;2)\cup(4;+\infty)" align="absmiddle" class="latex-formula">![log_{\frac{1}{3}}(x^2-6x+8)\geq-1\ \ \ \ \ \ \ 0<\frac{1}{3}<1\\x^2-6x+8\leq(\frac{1}{3})^{-1}\\x^2-6x+8\leq3\\x^2-6x+5\leq0\\(x-1)(x-5)\leq0\\x\in [1;5]](https://tex.z-dn.net/?f=log_%7B%5Cfrac%7B1%7D%7B3%7D%7D%28x%5E2-6x%2B8%29%5Cgeq-1%5C+%5C+%5C+%5C+%5C+%5C+%5C+0%3C%5Cfrac%7B1%7D%7B3%7D%3C1%5C%5Cx%5E2-6x%2B8%5Cleq%28%5Cfrac%7B1%7D%7B3%7D%29%5E%7B-1%7D%5C%5Cx%5E2-6x%2B8%5Cleq3%5C%5Cx%5E2-6x%2B5%5Cleq0%5C%5C%28x-1%29%28x-5%29%5Cleq0%5C%5Cx%5Cin+%5B1%3B5%5D "log_{\frac{1}{3}}(x^2-6x+8)\geq-1\ \ \ \ \ \ \ 0<\frac{1}{3}<1\\x^2-6x+8\leq(\frac{1}{3})^{-1}\\x^2-6x+8\leq3\\x^2-6x+5\leq0\\(x-1)(x-5)\leq0\\x\in [1;5]")