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[latex]9*3 \leq \frac{1}{9} * (\frac{1}{27} )^{ \frac{1}{x} } \ \ \ x\neq0!\\ 3^{2+1+2} \leq 27^{- \frac{1}{x}} \\ 3^5 \leq 3^{- \frac{3}{x} } \\ 3 \ \textgreater \ 1 =\ \textgreater \ 5 \leq -\frac{3}{x} \\ \frac{5x+3}{x} \leq 0 \\ -0.6 \leq x < 0[/latex]
[latex]7 \leq ( \frac{1}{49})^{\frac{2}{x}}*(\frac{1}{343})^{\frac{1}{x^2}}\\ 7^1 \leq 7^{-\frac{4}{x} -\frac{3}{x^2}} \\ 7 \ \textgreater \ 1 =\ \textgreater \ 1 \leq - \frac{4}{x} -\frac{3}{x^2} \\ \frac{x^2+4x+3}{x^2} \leq 0 \\ -3 \leq x \leq -1 [/latex]
[latex] \sqrt{32} *2^{-4x^2} \geq 8^{3x} \\ 2^{2.5-4x^2} \geq 2^{9x} \\ 2 \ \textgreater \ 1 =\ \textgreater \ 2.5-4x^2 \geq 9x \\ 8x^2 + 18x - 5 \leq 0 \\ x_{12} = \frac{-9 б \sqrt{81+40}}{8} = \frac{-9б\sqrt{121}}{8} = \frac{-9 б 11}{8} \\ x_1 = -2.5, x_2 = 0.25 \\ -2.5 \leq x \leq 0.25 [/latex]
[latex]125*(\frac{1}{5})^{x^2} \leq (\frac{1}{25})^{-4x}\\ 5^{3-x^2} \leq 5^{8x} \\ 5 \ \textgreater \ 1 =\ \textgreater \ 3-x^2 \leq 8x \\ x^2+8x-3 \geq 0\\ x_{12} = \frac{-4 б \sqrt{16+3}}{1} = -4 б \sqrt{19} \\ x \leq -4-\sqrt{19}, \ \ x \geq -4+\sqrt{19}[/latex]
[latex]log_{\frac{1}{9}}(x+8)+log_{\frac{1}{9}}x \geq -1 ,\ \ \ \ x \ \textgreater \ 0!\\ log_{\frac{1}{9}}(x^2+8x) \geq -1 \\ -0.5log_3(x^2+8x) \geq -1 \\ log_3(x^2+8x) \leq log_39\\ 3 \ \textgreater \ 1 =\ \textgreater \ x^2+8x \leq 9 \\ x^2+8x-9 \leq 0[/latex]
0 < x ≤ 1
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