\frac{1}{3}\cdot (1-log_2\frac{4}{7})" alt="1)\; \; \; 4^{-x+0,5}\cdot 7\cdot 2^{-x}-4<0\\\\2^{-2x+1}\cdot 2^{-x}\cdot 7<4\\\\2^{-3x+1}<\frac{4}{7}\; \; \; \to \; \; 2^{-3x+1}<2^{log_2{\frac{4}{7}}}\\\\-3x+1<log_2\frac{4}{7}\\\\x>\frac{1}{3}\cdot (1-log_2\frac{4}{7})" align="absmiddle" class="latex-formula">
0\; ,\; \; \; t^2+3<\frac{28}{3}t\; \; ,\; \; 3t^2-28t+9<0\; ,\\\\D/4=14^2-27=169\; ,\; \; t_{1,2}=\frac{14\pm 13}{3}\; \; ,\; \; t_1=\frac{1}{3}\; ,\; \; t_2=9\\\\3(t-\frac{1}{3})(t-9)<0\; \; \to \; \; t\in (\frac{1}{3}\, ,\, 9)\\\\3^{-1}<3^{\sqrt{x^2-3}}<3^2\; \; \to \; \; \; \; -1<\sqrt{x^2-3}<2\; \; \to \; \; \; 0\leq \sqrt{x^2-3}<2\; ,\\\\x^2-3<4\; ,\; \; x^2-7<0\; ,\; \; (x-\sqrt7)(x+\sqrt7)<0\; ," alt="2)\; \; \; 9^{\sqrt{x^2-3}}+3<28\cdot 3^{\sqrt{x^2-3}-1}\; ,\; \; ODZ:\; x^2-3\geq 0\; ,\\\\t=3^{\sqrt{x^2-3}}>0\; ,\; \; \; t^2+3<\frac{28}{3}t\; \; ,\; \; 3t^2-28t+9<0\; ,\\\\D/4=14^2-27=169\; ,\; \; t_{1,2}=\frac{14\pm 13}{3}\; \; ,\; \; t_1=\frac{1}{3}\; ,\; \; t_2=9\\\\3(t-\frac{1}{3})(t-9)<0\; \; \to \; \; t\in (\frac{1}{3}\, ,\, 9)\\\\3^{-1}<3^{\sqrt{x^2-3}}<3^2\; \; \to \; \; \; \; -1<\sqrt{x^2-3}<2\; \; \to \; \; \; 0\leq \sqrt{x^2-3}<2\; ,\\\\x^2-3<4\; ,\; \; x^2-7<0\; ,\; \; (x-\sqrt7)(x+\sqrt7)<0\; ," align="absmiddle" class="latex-formula">
![znaki:\; \; +++(-\sqrt7)---(\sqrt7)+++\qquad x\in (-\sqrt7,\sqrt7)\\\\\left \{ {{x^2-3\geq 0} \atop {x\in (-\sqrt7,\sqrt7)}} \right. \; \; \left \{ {{(x-\sqrt3)(x+\sqrt3)\geq 0} \atop {x\in (-\sqrt7,\sqrt7)}} \right. \; \; \left \{ {{x\in (-\infty ,-\sqrt3\, ]\cup [\, \sqrt3,+\infty )} \atop {x\in (-\sqrt7,\sqrt7)}} \right. \; \; \Rightarrow \\\\x\in (-\sqrt7,-\sqrt3\, ]\cup [\, \sqrt3,\sqrt7)](https://tex.z-dn.net/?f=znaki%3A%5C%3B%20%5C%3B%20%2B%2B%2B%28-%5Csqrt7%29---%28%5Csqrt7%29%2B%2B%2B%5Cqquad%20x%5Cin%20%28-%5Csqrt7%2C%5Csqrt7%29%5C%5C%5C%5C%5Cleft%20%5C%7B%20%7B%7Bx%5E2-3%5Cgeq%200%7D%20%5Catop%20%7Bx%5Cin%20%28-%5Csqrt7%2C%5Csqrt7%29%7D%7D%20%5Cright.%20%5C%3B%20%5C%3B%20%5Cleft%20%5C%7B%20%7B%7B%28x-%5Csqrt3%29%28x%2B%5Csqrt3%29%5Cgeq%200%7D%20%5Catop%20%7Bx%5Cin%20%28-%5Csqrt7%2C%5Csqrt7%29%7D%7D%20%5Cright.%20%5C%3B%20%5C%3B%20%5Cleft%20%5C%7B%20%7B%7Bx%5Cin%20%28-%5Cinfty%20%2C-%5Csqrt3%5C%2C%20%5D%5Ccup%20%5B%5C%2C%20%5Csqrt3%2C%2B%5Cinfty%20%29%7D%20%5Catop%20%7Bx%5Cin%20%28-%5Csqrt7%2C%5Csqrt7%29%7D%7D%20%5Cright.%20%5C%3B%20%5C%3B%20%5CRightarrow%20%5C%5C%5C%5Cx%5Cin%20%28-%5Csqrt7%2C-%5Csqrt3%5C%2C%20%5D%5Ccup%20%5B%5C%2C%20%5Csqrt3%2C%5Csqrt7%29 "znaki:\; \; +++(-\sqrt7)---(\sqrt7)+++\qquad x\in (-\sqrt7,\sqrt7)\\\\\left \{ {{x^2-3\geq 0} \atop {x\in (-\sqrt7,\sqrt7)}} \right. \; \; \left \{ {{(x-\sqrt3)(x+\sqrt3)\geq 0} \atop {x\in (-\sqrt7,\sqrt7)}} \right. \; \; \left \{ {{x\in (-\infty ,-\sqrt3\, ]\cup [\, \sqrt3,+\infty )} \atop {x\in (-\sqrt7,\sqrt7)}} \right. \; \; \Rightarrow \\\\x\in (-\sqrt7,-\sqrt3\, ]\cup [\, \sqrt3,\sqrt7)")
Если в примере №1 описка, и стоит не знак умножения перед 
, а знак плюс, то решение такое:
0\; \; ,\; \; 14t^2+t-4<0\; ,\; \; D=225" alt="3)\; \; 4^{-x+0,5}\cdot 7+2^{-x}-4<0\\\\2^{-2x+1}\cdot 7+2^{-x}-4<0\\\\t=2^{-x}>0\; \; ,\; \; 14t^2+t-4<0\; ,\; \; D=225" align="absmiddle" class="latex-formula">
0\; \; \to \; \; t\in (\, 0,\frac{1}{2})\\\\0<2^{-x}<\frac{1}{2}\; \; ,\; \; 0<2^{-x}<2^{-1}\; \; \Rightarrow \; \; -x<-1\; ,\\\\x>1" alt="t_1=\frac{-1-15}{2\cdot 14}=-\frac{4}{7}\; ,\; \; t_2=\frac{-1+15}{2\cdot 14}=\frac{1}{2}\\\\14\cdot (t+\frac{4}{7})(t-\frac{1}{2})<0\\\\znaki:\; \; \; +++(-\frac{4}{7})---(\frac{1}{2})+++\; \; \; t\in (-\frac{4}{7}\, ,\, \frac{1}{2})\\\\t>0\; \; \to \; \; t\in (\, 0,\frac{1}{2})\\\\0<2^{-x}<\frac{1}{2}\; \; ,\; \; 0<2^{-x}<2^{-1}\; \; \Rightarrow \; \; -x<-1\; ,\\\\x>1" align="absmiddle" class="latex-formula">