![1)\; \; (\frac{3}{4})^{x^2} \geq (\frac{4}{3})^{2x-3}\\\\(\frac{3}{4})^{x^2} \geq (\frac{3}{4})^{3-2x}\; \; \; \to \; \; \; x^2 \leq 3-2x\\\\x^2+2x-3 \leq 0\; ,\; \; \; x_1=-3,\; \; x_2=1\\\\(x+3)(x-1) \leq 0\\\\+++[-3]---[1]+++\\\\x\in [\, -3,1\, ]](https://tex.z-dn.net/?f=1%29%5C%3B+%5C%3B+%28%5Cfrac%7B3%7D%7B4%7D%29%5E%7Bx%5E2%7D+%5Cgeq+%28%5Cfrac%7B4%7D%7B3%7D%29%5E%7B2x-3%7D%5C%5C%5C%5C%28%5Cfrac%7B3%7D%7B4%7D%29%5E%7Bx%5E2%7D+%5Cgeq+%28%5Cfrac%7B3%7D%7B4%7D%29%5E%7B3-2x%7D%5C%3B+%5C%3B+%5C%3B+%5Cto+%5C%3B+%5C%3B+%5C%3B+x%5E2+%5Cleq+3-2x%5C%5C%5C%5Cx%5E2%2B2x-3+%5Cleq+0%5C%3B+%2C%5C%3B+%5C%3B+%5C%3B+x_1%3D-3%2C%5C%3B+%5C%3B+x_2%3D1%5C%5C%5C%5C%28x%2B3%29%28x-1%29+%5Cleq+0%5C%5C%5C%5C%2B%2B%2B%5B-3%5D---%5B1%5D%2B%2B%2B%5C%5C%5C%5Cx%5Cin+%5B%5C%2C+-3%2C1%5C%2C+%5D "1)\; \; (\frac{3}{4})^{x^2} \geq (\frac{4}{3})^{2x-3}\\\\(\frac{3}{4})^{x^2} \geq (\frac{3}{4})^{3-2x}\; \; \; \to \; \; \; x^2 \leq 3-2x\\\\x^2+2x-3 \leq 0\; ,\; \; \; x_1=-3,\; \; x_2=1\\\\(x+3)(x-1) \leq 0\\\\+++[-3]---[1]+++\\\\x\in [\, -3,1\, ]")
(\frac{3}{2})^{-1}\\\\2t> -1\\\\t> -\frac{1}{2}\\\\t\in (-\frac{1}{2},+\infty )" alt="2)\; \; 9^{t}+5\cdot 3^{2t}\ \textgreater \ 4^{t}+3\cdot 2^{2t}\\\\9=3^2\; ,\; 4=2^2\\\\3^{2t}+5\cdot 3^{2t}\ \textgreater \ 2^{2t}+3\cdot 2^{2t}\\\\6\cdot 3^{2t}\ \textgreater \ 4\cdot 2^{2t}\, |:2^{2t}\ \textgreater \ 0\\\\6\cdot \frac{3^{2t}}{2^{2t}}\ \textgreater \ 4\, |:6\ \textgreater \ 0\\\\(\frac{3}{2})^{2t}\ \textgreater \ \frac{4}{6}\; \; \; \; (\; \frac{4}{6}=\frac{2}{3}\; )\\\\(\frac{3}{2})^{2t}> (\frac{3}{2})^{-1}\\\\2t> -1\\\\t> -\frac{1}{2}\\\\t\in (-\frac{1}{2},+\infty )" align="absmiddle" class="latex-formula">