0\\\\-2\cdot \frac{log_327}{log_3{\frac{x}{3}}} \geq log_327+log_3x+1\\\\\frac{-2\cdot log_33^3}{log_3x-log_33} \geq log_33^3+log_3x+1\\\\\frac{-2\cdot 3}{log_3x-1} \geq 3+log_3x+1\\\\t=log_3x,\; \; \frac{-6}{t-1} \geq t+4,\; \; t\ne 1\\\\a)\; esli t-1>0,t>1\; to\; -6 \geq (t-1)(t+4),\\\\t^2+3t+2 \leq 0,\; \; (t+1)(t+2) \leq 0,\; \to \; -2 \leq t \leq -1\\\\ \left \{ {{-2\leg t \leq -1,} \atop {t >1}} \right. t\in \varnothing" alt="-2log_{\frac{x}{3}}27 \geq log_3{27x}+1,\; \; OOF:\; x>0\\\\-2\cdot \frac{log_327}{log_3{\frac{x}{3}}} \geq log_327+log_3x+1\\\\\frac{-2\cdot log_33^3}{log_3x-log_33} \geq log_33^3+log_3x+1\\\\\frac{-2\cdot 3}{log_3x-1} \geq 3+log_3x+1\\\\t=log_3x,\; \; \frac{-6}{t-1} \geq t+4,\; \; t\ne 1\\\\a)\; esli t-1>0,t>1\; to\; -6 \geq (t-1)(t+4),\\\\t^2+3t+2 \leq 0,\; \; (t+1)(t+2) \leq 0,\; \to \; -2 \leq t \leq -1\\\\ \left \{ {{-2\leg t \leq -1,} \atop {t >1}} \right. t\in \varnothing" align="absmiddle" class="latex-formula">
![b)esli\; \; t-1<0,\; t<1,\; to\; \; -6 \leq (t-1)(t+4)\\\\t^2+3t+2 \geq 0,\; \; (t+1)(t+2) \geq 0\; \; \to \; \; t \leq -2\; ili\; t \geq -1\; \to \; \\\\t\in (-\infty;-2]U[-1;1]\\\\log_3x \leq -2,\; x \leq \frac{1}{9}\\\\-1 \leq log_3x \leq 1,\; \; \frac{1}{3} \leq x \leq 3\\\\Otvet:\; x\in (-\infty;\frac{1}{9}]U[\frac{1}{3};3]](https://tex.z-dn.net/?f=+b%29esli%5C%3B+%5C%3B+t-1%3C0%2C%5C%3B+t%3C1%2C%5C%3B+to%5C%3B+%5C%3B+-6+%5Cleq+%28t-1%29%28t%2B4%29%5C%5C%5C%5Ct%5E2%2B3t%2B2+%5Cgeq+0%2C%5C%3B+%5C%3B+%28t%2B1%29%28t%2B2%29+%5Cgeq+0%5C%3B+%5C%3B+%5Cto+%5C%3B+%5C%3B+t+%5Cleq+-2%5C%3B+ili%5C%3B+t+%5Cgeq+-1%5C%3B+%5Cto+%5C%3B+%5C%5C%5C%5Ct%5Cin+%28-%5Cinfty%3B-2%5DU%5B-1%3B1%5D%5C%5C%5C%5Clog_3x+%5Cleq+-2%2C%5C%3B+x+%5Cleq+%5Cfrac%7B1%7D%7B9%7D%5C%5C%5C%5C-1+%5Cleq+log_3x+%5Cleq+1%2C%5C%3B+%5C%3B+%5Cfrac%7B1%7D%7B3%7D+%5Cleq+x+%5Cleq+3%5C%5C%5C%5COtvet%3A%5C%3B+x%5Cin+%28-%5Cinfty%3B%5Cfrac%7B1%7D%7B9%7D%5DU%5B%5Cfrac%7B1%7D%7B3%7D%3B3%5D "b)esli\; \; t-1<0,\; t<1,\; to\; \; -6 \leq (t-1)(t+4)\\\\t^2+3t+2 \geq 0,\; \; (t+1)(t+2) \geq 0\; \; \to \; \; t \leq -2\; ili\; t \geq -1\; \to \; \\\\t\in (-\infty;-2]U[-1;1]\\\\log_3x \leq -2,\; x \leq \frac{1}{9}\\\\-1 \leq log_3x \leq 1,\; \; \frac{1}{3} \leq x \leq 3\\\\Otvet:\; x\in (-\infty;\frac{1}{9}]U[\frac{1}{3};3]")