0, \\ x \ne 1. \end{cases}\\ \log_2x-2\frac{\log_22}{\log_2x}=-log_22\\ \frac{\log_2^2x-2+\log_2x}{\log_2x}=0\\ \log_2x=t\\ t^2+t-2=0\\ D=1+8=9 t_1=\frac{-1+3}{2}=1\\ t_2=\frac{-1-3}{2}=-2\\ log_2x=1, x=2\\ log_2x=-2, x=\frac{1}{4}" alt="\log_2x-2\log_x2=-1\\ \begin{cases} x>0, \\ x \ne 1. \end{cases}\\ \log_2x-2\frac{\log_22}{\log_2x}=-log_22\\ \frac{\log_2^2x-2+\log_2x}{\log_2x}=0\\ \log_2x=t\\ t^2+t-2=0\\ D=1+8=9 t_1=\frac{-1+3}{2}=1\\ t_2=\frac{-1-3}{2}=-2\\ log_2x=1, x=2\\ log_2x=-2, x=\frac{1}{4}" align="absmiddle" class="latex-formula">
0, \\ x \ne 1. \end{cases}\\ \log_2x+\frac{\log_22}{\log_2x}=2,5\\ \frac{\log_2^2x+1-2,5\log_2x}{\log_2x}=0\\ \log_2x=t\\ t^2-2,5t+1=0\\ D=2,5*2,5-4=2,25\\ t_1=\frac{2,5+1,5}{2}=2\\ t_2=\frac{2,5-1,5}{2}=\frac{1}{2}\\ log_2x=2, x=4\\ log_2x=\frac{1}{2}, x=\sqrt{2}" alt="\log_2x+\log_x2=2,5\\ \begin{cases} x>0, \\ x \ne 1. \end{cases}\\ \log_2x+\frac{\log_22}{\log_2x}=2,5\\ \frac{\log_2^2x+1-2,5\log_2x}{\log_2x}=0\\ \log_2x=t\\ t^2-2,5t+1=0\\ D=2,5*2,5-4=2,25\\ t_1=\frac{2,5+1,5}{2}=2\\ t_2=\frac{2,5-1,5}{2}=\frac{1}{2}\\ log_2x=2, x=4\\ log_2x=\frac{1}{2}, x=\sqrt{2}" align="absmiddle" class="latex-formula">
0, \\ x \ne 1. \end{cases}\\ \log_3x+2\frac{\log_33}{\log_3x}=3\\ \frac{\log_3^2x+2-3\log_3x}{\log_3x}=0\\ \log_3x=t\\ t^2-3t+2=0\\ D=9-8=1\\ t_1=\frac{3+1}{2}=2\\ t_2=\frac{3-1}{2}=1\\ log_3x=2, x=9\\ log_3x=1, x=3" alt="\log_3x+2\log_x3=3\\ \begin{cases} x>0, \\ x \ne 1. \end{cases}\\ \log_3x+2\frac{\log_33}{\log_3x}=3\\ \frac{\log_3^2x+2-3\log_3x}{\log_3x}=0\\ \log_3x=t\\ t^2-3t+2=0\\ D=9-8=1\\ t_1=\frac{3+1}{2}=2\\ t_2=\frac{3-1}{2}=1\\ log_3x=2, x=9\\ log_3x=1, x=3" align="absmiddle" class="latex-formula">
0, \\ x \ne 1. \end{cases}\\ \log_3x-6\frac{\log_33}{\log_3x}=1\\ \frac{\log_3^2x-6-\log_3x}{\log_3x}=0\\ \log_3x=t\\ t^2-t-6=0\\ D=25\\ t_1=\frac{1+5}{2}=3\\ t_2=\frac{1-5}{2}=-2\\ log_3x=3, x=27\\ log_3x=-2, x=\frac{1}{9}" alt="\log_3x-6\log_x3=1\\ \begin{cases} x>0, \\ x \ne 1. \end{cases}\\ \log_3x-6\frac{\log_33}{\log_3x}=1\\ \frac{\log_3^2x-6-\log_3x}{\log_3x}=0\\ \log_3x=t\\ t^2-t-6=0\\ D=25\\ t_1=\frac{1+5}{2}=3\\ t_2=\frac{1-5}{2}=-2\\ log_3x=3, x=27\\ log_3x=-2, x=\frac{1}{9}" align="absmiddle" class="latex-formula">