![\displaystyle \tt 12.\\\\1). \ \ 2^{2x}=\frac{1}{\sqrt[3]{4}}\\\\{} \ \ \ \ \ \ 2^{2x}=2^{-2/3}\\\\{} \ \ \ \ \ \ 2x=-\frac{2}{3}\\\\{} \ \ \ \ \ \ x=- \frac{1}{3} \\\\\\2). \ \ 4\cdot\bigg(\frac{3}{2}\bigg)^{x}=9\\\\\\{} \ \ \ \ \ \ \bigg(\frac{3}{2}\bigg)^{x}= \frac{9}{4}\\\\\\{} \ \ \ \ \ \ \bigg(\frac{3}{2}\bigg)^{x}= \bigg(\frac{3}{2}\bigg)^{2}\\\\\\{} \ \ \ \ \ \ x=2](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ctt%2012.%5C%5C%5C%5C1%29.%20%5C%20%5C%202%5E%7B2x%7D%3D%5Cfrac%7B1%7D%7B%5Csqrt%5B3%5D%7B4%7D%7D%5C%5C%5C%5C%7B%7D%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%202%5E%7B2x%7D%3D2%5E%7B-2%2F3%7D%5C%5C%5C%5C%7B%7D%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%202x%3D-%5Cfrac%7B2%7D%7B3%7D%5C%5C%5C%5C%7B%7D%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20x%3D-%20%5Cfrac%7B1%7D%7B3%7D%20%5C%5C%5C%5C%5C%5C2%29.%20%5C%20%5C%204%5Ccdot%5Cbigg%28%5Cfrac%7B3%7D%7B2%7D%5Cbigg%29%5E%7Bx%7D%3D9%5C%5C%5C%5C%5C%5C%7B%7D%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5Cbigg%28%5Cfrac%7B3%7D%7B2%7D%5Cbigg%29%5E%7Bx%7D%3D%20%5Cfrac%7B9%7D%7B4%7D%5C%5C%5C%5C%5C%5C%7B%7D%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5Cbigg%28%5Cfrac%7B3%7D%7B2%7D%5Cbigg%29%5E%7Bx%7D%3D%20%5Cbigg%28%5Cfrac%7B3%7D%7B2%7D%5Cbigg%29%5E%7B2%7D%5C%5C%5C%5C%5C%5C%7B%7D%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20x%3D2 "\displaystyle \tt 12.\\\\1). \ \ 2^{2x}=\frac{1}{\sqrt[3]{4}}\\\\{} \ \ \ \ \ \ 2^{2x}=2^{-2/3}\\\\{} \ \ \ \ \ \ 2x=-\frac{2}{3}\\\\{} \ \ \ \ \ \ x=- \frac{1}{3} \\\\\\2). \ \ 4\cdot\bigg(\frac{3}{2}\bigg)^{x}=9\\\\\\{} \ \ \ \ \ \ \bigg(\frac{3}{2}\bigg)^{x}= \frac{9}{4}\\\\\\{} \ \ \ \ \ \ \bigg(\frac{3}{2}\bigg)^{x}= \bigg(\frac{3}{2}\bigg)^{2}\\\\\\{} \ \ \ \ \ \ x=2")
1\\\\{} \ \ \ \ \ \ 2^{-x}>2^{0}\\\\{} \ \ \ \ \ \ x<0\\\\{} \ \ \ \ \ \ x\in(-\infty;0)\\\\\\2). \ \ 3^{x}<9\\\\{} \ \ \ \ \ \ 3^{x}<3^{2}\\\\{} \ \ \ \ \ \ x<2\\\\{} \ \ \ \ \ \ x\in(-\infty;2)\\\\\\3). \ \ 2^{3x}\geq \frac{1}{2}\\\\{} \ \ \ \ \ \ 2^{3x}\geq2^{-1}\\\\{} \ \ \ \ \ \ 3x \geq-1\\\\{} \ \ \ \ \ \ x \geq- \frac{1}{3}\\\\{} \ \ \ \ \ \ x\in[-\frac{1}{3};\infty)" alt="\displaystyle \tt 13.\\\\1). \ \ (0,5)^{x}>1\\\\{} \ \ \ \ \ \ 2^{-x}>2^{0}\\\\{} \ \ \ \ \ \ x<0\\\\{} \ \ \ \ \ \ x\in(-\infty;0)\\\\\\2). \ \ 3^{x}<9\\\\{} \ \ \ \ \ \ 3^{x}<3^{2}\\\\{} \ \ \ \ \ \ x<2\\\\{} \ \ \ \ \ \ x\in(-\infty;2)\\\\\\3). \ \ 2^{3x}\geq \frac{1}{2}\\\\{} \ \ \ \ \ \ 2^{3x}\geq2^{-1}\\\\{} \ \ \ \ \ \ 3x \geq-1\\\\{} \ \ \ \ \ \ x \geq- \frac{1}{3}\\\\{} \ \ \ \ \ \ x\in[-\frac{1}{3};\infty)" align="absmiddle" class="latex-formula">
