0} \atop {3x-2>0}} \right. \; \Rightarrow \; x>\frac{2}{3}\\\\lg\frac{3x^2+28}{3x-2}=lg10\; \; \Rightarrow \; \; \frac{3x^2+28}{3x-2}=10\; ,\; \; \frac{3x^2+28-30x+20}{3x-2} =0\; ,\\\\3x^2-30x+48=0\; ,\; \; x^2-10x+16=0\; ,\; \; \underline {x_1=2\; ,\; x_2=8}\\\\\\54.6)\; \; lg(x^2+1)-lg(x-2)=1\; ,\; \; ODZ:\; \left \{ {{x^2+1>0} \atop {x-2>0}} \right. \; \Rightarrow \; x>2" alt="54.1)\; \; lg(3x^2+28)-lg(3x-2)=1\; ,\; \; ODZ:\; \left \{ {{3x^2+28>0} \atop {3x-2>0}} \right. \; \Rightarrow \; x>\frac{2}{3}\\\\lg\frac{3x^2+28}{3x-2}=lg10\; \; \Rightarrow \; \; \frac{3x^2+28}{3x-2}=10\; ,\; \; \frac{3x^2+28-30x+20}{3x-2} =0\; ,\\\\3x^2-30x+48=0\; ,\; \; x^2-10x+16=0\; ,\; \; \underline {x_1=2\; ,\; x_2=8}\\\\\\54.6)\; \; lg(x^2+1)-lg(x-2)=1\; ,\; \; ODZ:\; \left \{ {{x^2+1>0} \atop {x-2>0}} \right. \; \Rightarrow \; x>2" align="absmiddle" class="latex-formula">
0\; ,\\\\D<0\; \to \; \; x\in R\\\\2^{lg(x^2-6x+10\sqrt{10})}=2^{3/2}\; ,\; \; lg(x^2-6x+10\sqrt{10})=\frac{3}{2}\; ,\\\\x^2-6x+10\sqrt{10}=10^{3/2}\; ,\; \; x^2-6x+10\sqrt{10}=10\sqrt{10}\; ,\\\\x^2-6x=0\; ,\; \; x(x-6)=0\; ,\\\\\underline {x_1=0\; ,\; \; x_2=6}" alt="lg\frac{x^2+1}{x-2}=lg10\; ,\; \; \frac{x^2+1}{x-2}=10\; ,\; \frac{x^2+1-10x+20}{x-2} =0\; ,\; \frac{x^2-10x+21}{x-2}=0\; ,\\\\x^2-10x+21=0\; \; \Rightarrow \; \; \; \underline {x_1=3\; ,\; \; x_2=7}\; \; (teor.\; Vieta)\\\\\\55.3)\; \; 2^{lg(x^2-6x+10\sqrt{10})}=2\sqrt2\; ,\; \; ODZ:\; x^2-6x+10\sqrt{10}>0\; ,\\\\D<0\; \to \; \; x\in R\\\\2^{lg(x^2-6x+10\sqrt{10})}=2^{3/2}\; ,\; \; lg(x^2-6x+10\sqrt{10})=\frac{3}{2}\; ,\\\\x^2-6x+10\sqrt{10}=10^{3/2}\; ,\; \; x^2-6x+10\sqrt{10}=10\sqrt{10}\; ,\\\\x^2-6x=0\; ,\; \; x(x-6)=0\; ,\\\\\underline {x_1=0\; ,\; \; x_2=6}" align="absmiddle" class="latex-formula">