0;\\ lg x=t;\\ t^2-t-2=0;\\ D=(-1)^2-4*1*(-2)=9=3^2;\\ t_1=\frac{-(-1)-3}{2*1}=-1;\\ t_2=\frac{-(-1)+3}{2*1}=2;\\ lg x=-1;\\ x_1=10^{-1}=0.1;\\ lg x=2;\\ x_2=10^2=100" alt="(lg x)^2-lg x=2;\\ x>0;\\ lg x=t;\\ t^2-t-2=0;\\ D=(-1)^2-4*1*(-2)=9=3^2;\\ t_1=\frac{-(-1)-3}{2*1}=-1;\\ t_2=\frac{-(-1)+3}{2*1}=2;\\ lg x=-1;\\ x_1=10^{-1}=0.1;\\ lg x=2;\\ x_2=10^2=100" align="absmiddle" class="latex-formula">
0;\\ 3^x-27=0;\\ 3^x=27;\\ 3^x=3^3;\\ x=3 " alt="3^{2x-3}-8*3^{x-2}=3;\\ 3^{2x}*3^{-3}-8*3^x*3^{-2}=3; |*27\\ 3^{2x}-24*3^x-81=0;\\ (3^x-27)(3^x+3)=0;\\ 3^x+3>0;\\ 3^x-27=0;\\ 3^x=27;\\ 3^x=3^3;\\ x=3 " align="absmiddle" class="latex-formula">
0; x \neq 1;\\ log_2 x- log_x 2^2=3;\\ log_2 x-2 log_x 2=3;\\ log_2 x-\frac{2}{log_2 x}-3=0;\\ \frac{log^2_2 x-3log_2 x-2}{log_2 x}=0; log^2_2 x-3log_2 x-2=0;\\ log_2 x=t;\\ t^2-3t-2=0;\\ D=(-3)^2-4*1*(-2)=17;\\ t_1=\frac{3-\sqrt{17}}{2};\\ t_2=\frac{3+\sqrt{17}}{2};\\ x_1=2^{\frac{3-\sqrt{17}}{2}};\\ x_1=2^{\frac{3+\sqrt{17}}{2}};\\" alt="log_2 x-log_x 4=3;\\ x>0; x \neq 1;\\ log_2 x- log_x 2^2=3;\\ log_2 x-2 log_x 2=3;\\ log_2 x-\frac{2}{log_2 x}-3=0;\\ \frac{log^2_2 x-3log_2 x-2}{log_2 x}=0; log^2_2 x-3log_2 x-2=0;\\ log_2 x=t;\\ t^2-3t-2=0;\\ D=(-3)^2-4*1*(-2)=17;\\ t_1=\frac{3-\sqrt{17}}{2};\\ t_2=\frac{3+\sqrt{17}}{2};\\ x_1=2^{\frac{3-\sqrt{17}}{2}};\\ x_1=2^{\frac{3+\sqrt{17}}{2}};\\" align="absmiddle" class="latex-formula">
0; x> 0.2;\\ log_2 (5x-1)-1=t \neq 0;\\ t+1-\frac{3}{t}+1=0;\\ t-\frac{3}{t}+2=0;\\ t^2+2t-3=0;\\ (t+3)(t-2)=0;\\ t_1=-3; t_2=2; log_2 (5x-1)-1=-3;\\ log_2 (5x-1)=-2;\\ 5x-1=2^{-2};\\ 5x-1=0.25;\\ 5x=1.25;\\ x_1=0.25;\\ log_2 (5x-1)-1=2;\\ log_2 (5x-1)=3;\\ 5x-1=2^3;\\ 5x-1=8;\\ 5x=9;\\ x_2=1.4\\" alt="log_2 (5x-1)-\frac{3}{log_2 (5x-1)-1}+1=0;\\ 5x-1>0; x> 0.2;\\ log_2 (5x-1)-1=t \neq 0;\\ t+1-\frac{3}{t}+1=0;\\ t-\frac{3}{t}+2=0;\\ t^2+2t-3=0;\\ (t+3)(t-2)=0;\\ t_1=-3; t_2=2; log_2 (5x-1)-1=-3;\\ log_2 (5x-1)=-2;\\ 5x-1=2^{-2};\\ 5x-1=0.25;\\ 5x=1.25;\\ x_1=0.25;\\ log_2 (5x-1)-1=2;\\ log_2 (5x-1)=3;\\ 5x-1=2^3;\\ 5x-1=8;\\ 5x=9;\\ x_2=1.4\\" align="absmiddle" class="latex-formula">
0;\\ t^2-3.8t-6=0;\\ D=(-3.8)^2-4*1*(-6)=38.44=6.2^2;\\ t_1=\frac{3.8-6.2}{2*1}<0;\\ t_2=\frac{3.8+6.2}{2*1}=5;\\ 5^x=5;\\ 5^x=5^1;\\ x=1\\ " alt="5^x-6*5^{-x}=3.8; |*5^x;\\ 5^{2x}-3.8*5^x-6=0;\\ 5^x=t>0;\\ t^2-3.8t-6=0;\\ D=(-3.8)^2-4*1*(-6)=38.44=6.2^2;\\ t_1=\frac{3.8-6.2}{2*1}<0;\\ t_2=\frac{3.8+6.2}{2*1}=5;\\ 5^x=5;\\ 5^x=5^1;\\ x=1\\ " align="absmiddle" class="latex-formula">