Показательные уравнения 1)[latex]( \sqrt[3]{5} ) ^{-3x+6} =25 ^{x+4} [/latex] 2)[latex]6*25^x+5*36^x=11*30^x[/latex] 3)[latex]6 ^{2x+1} = \sqrt{6} ^{-4x+3} [/latex] 4)[latex]7*49^x=50*7^x-7[/latex]

[latex](\sqrt[3]{5})^{-3x+6}=25^{x+4}\\ \\(5^\frac{1}{3})^{3(2-x)}=5^{2(x+4)}\\ \\5^{(2-x)}=5^{2(x+4)}\\ \\2-x=2(x+4)\\ \\2-x=2x+8\\ \\-x-2x=8-2\\ \\-3x=6\\ \\x=-2\\[/latex] [latex]6*25^x+5*36^x=11*30^x\\ \\6*5^{2x}+5*6^{2x}=11*5^x*6^x|/5^x*6^x\\ \\6*\frac{5^x}{6^x}+5*\frac{6^x}{5^x}=11\\ \\\frac{5^x}{6^x}=t\\ \\6*t+5/t=11|*t\\ \\6t^2+5=11t\\ \\6t^2-11t+5=00\\ \\D=121-4*5*6=1\\ \\\sqrt1=1\\ \\t_1=\frac{11+1}{12}=1\\ \\t_2=\frac{11-1}{12}=\frac{10}{12}=\frac{5}{6}\\ \\\frac{5^x}{6^x}=1\\ \\=\ \textgreater \ x_1=0\\ \\\frac{5^x}{6^x}=\frac{5}{6}\\ \\=\ \textgreater \ x_2=1\\[/latex] [latex] 6^{2x+1}=\sqrt{6}^{-4x+3}\\ 6^{2x+1}=6^{-2x+1.5}\\ 2x+1=-2x+1.5\\ 4x=0.5\\ x=0.125\\ [/latex] [latex]7*49^x=50*7^x-7 7*7^{2x}=50*7^x-7\\ 7*7^{2x}-50*7^{x}=-7\\ 7^x=t\\ 7t^2-50t+7=0\\ D=2500-4*49=2304\\ \sqrt{2304}=48\\ t_1=(50-48)/14=1/7\\ t_2=98/14=7\\ 7^x=1/7\\ x=-1\\ 7^x=7\\ x=1\\[/latex]

1) [latex] \sqrt[3]{5}^{-3x+6}=25^{x+4} 5^{-x}*5^2=5^{2x}*5^8 5^{-x}=5^{2x}*5^6 5^{3x}=5^{-6} 5^x=5^{-2} x=-2[/latex] 2) [latex]6*25^x+5*36^x=11*30^x 6*5^{2x}+5*6^{2x}=11*(5*6)^x 6*(5/6)^x+5*(6/5)^x=11 (5/6)^x=t 6t+5/t=11 6t^2+5-11t=0 D=121-120=1 t=(11+1)/12=1; t=(11-1)/12=5/6 (5/6)^x=1; x=0 (5/6)^x=5/6; x=1[/latex] 3) [latex]6^{2x+1}=((6)^{1/2})^{-4x+3} 6^{2x}*6=6^{-2x}*6^{3/2} 6^{2x}=t 6t=6^{3/2}/t 6t^2=6^{3/2} t^2=6^{1/2} t=6^{1/4} 6^{2x}=6^{1/4} 2x=1/4 x=1/8 [/latex] 4)  [latex]7*7^{2x}=50*7^x-7 7^x=t 7t^2-50t+7=0 D=2500-196=48^2 t=7; t=1/7 7^x=7; x=1 7^x=1/7; x=-1[/latex]