(0,5)^{-1}\\2^3\cdot2^{x^2-3x}>\left(\frac12\right)^{-1}\\2^{x^2-3x+3}>2^1\\x^2-3x+3>1\\x^2-3x+2>0\\(x-1)(x-2)>0\\x\in(-\infty;\;1)\cup(2;\;+\infty)\\\\3)\;2\log_{0,4}(x-2)\geq\log_{0,4}(x+4)\\O.D.3.:\\\begin{cases}x-2>0\\x+4>0\end{cases}\Rightarrow\begin{cases}x>2\\x>-4\end{cases}\Rightarrow x>2" alt="1)\;27^x\leq\left(\frac13\right)^{-6}\\(3^3)^x\leq3^6\\3^{3x}\leq6\\3x\leq6\\x\leq2\\\\2)\;8\cdot2^{x^2-3x}>(0,5)^{-1}\\2^3\cdot2^{x^2-3x}>\left(\frac12\right)^{-1}\\2^{x^2-3x+3}>2^1\\x^2-3x+3>1\\x^2-3x+2>0\\(x-1)(x-2)>0\\x\in(-\infty;\;1)\cup(2;\;+\infty)\\\\3)\;2\log_{0,4}(x-2)\geq\log_{0,4}(x+4)\\O.D.3.:\\\begin{cases}x-2>0\\x+4>0\end{cases}\Rightarrow\begin{cases}x>2\\x>-4\end{cases}\Rightarrow x>2" align="absmiddle" class="latex-formula">
![\log_{0,4}(x-2)^2\geq\log_{0,4}(x+4)\\(x-2)^2\leq x+4\\x^2-4x+4\leq x+4\\x^2-5x\leq0\\x(x-5)\leq0\\x\in[0;\;5]\\C\;O.D.3.\;x\in(2;\;5]](https://tex.z-dn.net/?f=%5Clog_%7B0%2C4%7D%28x-2%29%5E2%5Cgeq%5Clog_%7B0%2C4%7D%28x%2B4%29%5C%5C%28x-2%29%5E2%5Cleq%20x%2B4%5C%5Cx%5E2-4x%2B4%5Cleq%20x%2B4%5C%5Cx%5E2-5x%5Cleq0%5C%5Cx%28x-5%29%5Cleq0%5C%5Cx%5Cin%5B0%3B%5C%3B5%5D%5C%5CC%5C%3BO.D.3.%5C%3Bx%5Cin%282%3B%5C%3B5%5D "\log_{0,4}(x-2)^2\geq\log_{0,4}(x+4)\\(x-2)^2\leq x+4\\x^2-4x+4\leq x+4\\x^2-5x\leq0\\x(x-5)\leq0\\x\in[0;\;5]\\C\;O.D.3.\;x\in(2;\;5]")