0\; ,\; \; t^3+t^2-3t-3\geq 0\; ,\\\\t^2(t+1)-3(t+1)\geq 0\; ,\; \; (t+1)(t^2-3)\geq 0\; ,\\\\(t+1)(t-\sqrt3)(t+\sqrt3)\geq 0" alt="3^{3x}-3^{x+1}\cdot 2^{2x}+18^{x}-3\cdot 8^{x}\geq 0\\\\3^{3x}-3\cdot 3^{x}\cdot 2^{2x}+2^{x}\cdot 3^{2x}-3\cdot 2^{3x}\geq 0\; \Big |\, :2^{3x}\ne 0\\\\\frac{3^{3x}}{2^{3x}}-3\cdot \frac{3^{x}\cdot 2^{2x}}{2^{3x}}+\frac{2^{x}\cdot 3^{2x}}{2^{3x}}-\frac{3\cdot 2^{3x}}{2^{3x}}\geq 0\\\\(\frac{3}{2})^{3x}-3\cdot (\frac{3}{2})^{x}+(\frac{3}{2})^{2x}-3\geq 0\\\\t=(\frac{3}{2})^{x}>0\; ,\; \; t^3+t^2-3t-3\geq 0\; ,\\\\t^2(t+1)-3(t+1)\geq 0\; ,\; \; (t+1)(t^2-3)\geq 0\; ,\\\\(t+1)(t-\sqrt3)(t+\sqrt3)\geq 0" align="absmiddle" class="latex-formula">
0\; \; \Rightarrow \\\\t\in [\, \sqrt3;+\infty )\; \; \Rightarrow \; \; (\frac{3}{2})^{x}\geq \sqrt3\; \; \Rightarrow \; \; \; x\geq log_{3/2}\sqrt3\; \; ,\\\\x\geq \frac{log_3\sqrt3}{log_3(3/2)}\; \; ,\; \; x\geq \frac{1/2}{1-log_32}\; \; ,\\\\x\geq \frac{1}{2\, (1-log_32)}" alt="znaki:\; \; ---[-\sqrt3\, ]+++[-1]---[\, \sqrt3\, ]+++\\\\t\in [-\sqrt3;-1\, ]\cup [\, \sqrt3;+\infty )\; \; \; i\; \; \; t>0\; \; \Rightarrow \\\\t\in [\, \sqrt3;+\infty )\; \; \Rightarrow \; \; (\frac{3}{2})^{x}\geq \sqrt3\; \; \Rightarrow \; \; \; x\geq log_{3/2}\sqrt3\; \; ,\\\\x\geq \frac{log_3\sqrt3}{log_3(3/2)}\; \; ,\; \; x\geq \frac{1/2}{1-log_32}\; \; ,\\\\x\geq \frac{1}{2\, (1-log_32)}" align="absmiddle" class="latex-formula">