0\; pri\; x\in R\\\\5^{x}=10,\; x=log_510=1+log_52\\\\2)log_{\frac{1}{3}}(7x-1)>0,\; OOF:\; 7x-1>0,x>\frac{1}{7}\\\\7x-1<1,\; x<\frac{2}{7}\\\\Otvet:\; x\in (\frac{1}{7},\frac{2}{7})" alt="25^{x}-5^{x+1} \geq 50\\\\(5^{x})^2-5\cdot 5^{x}-50 \geq 0\\\\D=225,5^{x}=\frac{5-15}{2}=-5<0\; ne\; podxodit,t.k.\; 5^{x}>0\; pri\; x\in R\\\\5^{x}=10,\; x=log_510=1+log_52\\\\2)log_{\frac{1}{3}}(7x-1)>0,\; OOF:\; 7x-1>0,x>\frac{1}{7}\\\\7x-1<1,\; x<\frac{2}{7}\\\\Otvet:\; x\in (\frac{1}{7},\frac{2}{7})" align="absmiddle" class="latex-formula">
0} \atop {x+1>0}} \right. \; x>1\\\\log_3(x-1)(x+1)=log_33\\\\x^2-1=3\\\\x^2-4=0\\\\(x-2)(x+2)=0\\\\x=-2\; \notin OOF\\\\x=2\in OOF" alt="3)\; log_3(x-1)+log_3(x+1)=1,\; OOF:\; \left \{ {{x-1>0} \atop {x+1>0}} \right. \; x>1\\\\log_3(x-1)(x+1)=log_33\\\\x^2-1=3\\\\x^2-4=0\\\\(x-2)(x+2)=0\\\\x=-2\; \notin OOF\\\\x=2\in OOF" align="absmiddle" class="latex-formula">