1)
0, \\ 2^x>-1, \\ x\in R, \\ \lg2^{x-1}+\lg(1+2^x)=1, \\ \lg(2^{x-1}(1+2^x))=\lg10, \\ \frac{2^x}{2}(1+2^x)=10, \\ 2^x+2^{2x}=20, \\ 2^{2x}+2^x-20=0, \\ 2^x=t, t>0,\\ t^2+t-20=0, \\ t_1=-5<0, t_2=4, \\ 2^x=4, \\ 2^x=2^2,\\ x=2. " alt="(x-1)\lg2=1-\lg(1+2^x), \\ 1+2^x>0, \\ 2^x>-1, \\ x\in R, \\ \lg2^{x-1}+\lg(1+2^x)=1, \\ \lg(2^{x-1}(1+2^x))=\lg10, \\ \frac{2^x}{2}(1+2^x)=10, \\ 2^x+2^{2x}=20, \\ 2^{2x}+2^x-20=0, \\ 2^x=t, t>0,\\ t^2+t-20=0, \\ t_1=-5<0, t_2=4, \\ 2^x=4, \\ 2^x=2^2,\\ x=2. " align="absmiddle" class="latex-formula">
2)
3)
4)
5)
0, y\neq0,\\ \left \{ {{y=1+\log_4x,} \atop {\log_4x^y=\log_44^6;}} \right.\ \left \{ {{y=1+\log_4x,} \atop {y\log_4x=6\log_44;}} \right.\ \left \{ {{y=1+\log_4x,} \atop {y\log_4x=6;}} \right.\ \left \{ {{\log_4x=y-1,} \atop {\log_4x=\frac{6}{y};}} \right.\\ y-1=\frac{6}{y}, \\ y^2-y-6=0, \\ y_1=-2, y_2=3, \\ \log_4x=-3, x=4^{-3}, x_1=\frac{1}{64}, \\ \log_4x=2, x=4^2, x_2=8, \\ (\frac{1}{64};-2), (8;3)." alt="\left \{ {{y=1+\log_4x,} \atop {x^y=4^6;}} \right. \\ x>0, y\neq0,\\ \left \{ {{y=1+\log_4x,} \atop {\log_4x^y=\log_44^6;}} \right.\ \left \{ {{y=1+\log_4x,} \atop {y\log_4x=6\log_44;}} \right.\ \left \{ {{y=1+\log_4x,} \atop {y\log_4x=6;}} \right.\ \left \{ {{\log_4x=y-1,} \atop {\log_4x=\frac{6}{y};}} \right.\\ y-1=\frac{6}{y}, \\ y^2-y-6=0, \\ y_1=-2, y_2=3, \\ \log_4x=-3, x=4^{-3}, x_1=\frac{1}{64}, \\ \log_4x=2, x=4^2, x_2=8, \\ (\frac{1}{64};-2), (8;3)." align="absmiddle" class="latex-formula">
6)