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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">
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![x+4<\sqrt{-x^2-8x-12}, \\ -x^2-8x-12\geq0, \\ x^2+8x+12\leq0, \\ x^2+8x+12=0, x_1=-6, x_2=-2, \\ x\in[-6;-2]; \\ (x+4)^2<-x^2-8x-12, \\ x^2+8x+16<-x^2-8x-12, \\ 2x^2+16x+28<0, \\ x^2+8x+14<0, \\ x^2+8x+14=0, \\ D_{/4}=2, \\ x_1=-4-\sqrt2\approx-5,4, x_2=-4+\sqrt2\approx-2,6, \\ x\in(-4-\sqrt2;-4+\sqrt2). \\ max x\in Z=-3, \\ x^3+x^2=-27+9=-18. x+4<\sqrt{-x^2-8x-12}, \\ -x^2-8x-12\geq0, \\ x^2+8x+12\leq0, \\ x^2+8x+12=0, x_1=-6, x_2=-2, \\ x\in[-6;-2]; \\ (x+4)^2<-x^2-8x-12, \\ x^2+8x+16<-x^2-8x-12, \\ 2x^2+16x+28<0, \\ x^2+8x+14<0, \\ x^2+8x+14=0, \\ D_{/4}=2, \\ x_1=-4-\sqrt2\approx-5,4, x_2=-4+\sqrt2\approx-2,6, \\ x\in(-4-\sqrt2;-4+\sqrt2). \\ max x\in Z=-3, \\ x^3+x^2=-27+9=-18.](https://tex.z-dn.net/?f=x%2B4%3C%5Csqrt%7B-x%5E2-8x-12%7D%2C+%5C%5C+-x%5E2-8x-12%5Cgeq0%2C+%5C%5C+x%5E2%2B8x%2B12%5Cleq0%2C+%5C%5C+x%5E2%2B8x%2B12%3D0%2C+x_1%3D-6%2C+x_2%3D-2%2C+%5C%5C+x%5Cin%5B-6%3B-2%5D%3B+%5C%5C+%28x%2B4%29%5E2%3C-x%5E2-8x-12%2C+%5C%5C+x%5E2%2B8x%2B16%3C-x%5E2-8x-12%2C+%5C%5C+2x%5E2%2B16x%2B28%3C0%2C+%5C%5C+x%5E2%2B8x%2B14%3C0%2C+%5C%5C+x%5E2%2B8x%2B14%3D0%2C+%5C%5C+D_%7B%2F4%7D%3D2%2C+%5C%5C+x_1%3D-4-%5Csqrt2%5Capprox-5%2C4%2C+x_2%3D-4%2B%5Csqrt2%5Capprox-2%2C6%2C+%5C%5C+x%5Cin%28-4-%5Csqrt2%3B-4%2B%5Csqrt2%29.+%5C%5C+max+x%5Cin+Z%3D-3%2C+%5C%5C+x%5E3%2Bx%5E2%3D-27%2B9%3D-18.+)
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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">
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