Помогите пожалуйста,заранее спасибо. Решить уравнения 1)[latex]7*3 ^{x+1} -5 ^{x+2} = 3^{x+4} -5 ^{x+3} [/latex] 2)[latex]( \sqrt{2- \sqrt{3} } ) ^{x} +( \sqrt{2+ \sqrt{3} } ) ^{x}=4[/latex] 3)[latex]3*4 ^{x} -5*6 ^{x} +2*9 ^{x...

1) [latex] 5^{x+3} -5^{x+2}=3^{x+4}-7*3^{x+1}[/latex] [latex]5^{x+1}(25-5 )=3^{x+1}(27-7)[/latex] [latex] ( \frac{5}{3})^{x+1} = \frac{20}{20} =1[/latex] [latex]x+1=0[/latex] [latex]x=-1[/latex] 2)[latex]( \sqrt{2+ \sqrt{3} } ) ^{x} =t, t\ \textgreater \ 0[/latex] [latex]( \sqrt{2- \sqrt{3} } ) ^{x}= \frac{1}{t} [/latex] [latex] \frac{1}{t} +t=4[/latex] [latex] t^{2} -4t+1=0[/latex] [latex] t_{1} = 2+\sqrt{4-1}=2+ \sqrt{3}[/latex] [latex] (2+ \sqrt{3}) ^{ \frac{x}{2} } = (2+ \sqrt{3})^1 }[/latex] [latex] \frac{x}{2} =1[/latex] [latex]x=2[/latex] [latex]t_{2} =2- \sqrt{3}[/latex] [latex] (2- \sqrt{3}) ^{ \frac{x}{2} } = (2- \sqrt{3})^{-1} [/latex] [latex] \frac{x}{2} =-1[/latex] [latex]x=-2[/latex] [latex] x_{1}=-2 , x_{2} =2[/latex] 3)[latex]3* 2^{2x}-5 (2*3)^{x} +2* 3^{2x}=0 |/ 3^{2x} [/latex] [latex]3* ( \frac{2}{3} )^{2x} -5*( \frac{2}{3} )^{x}+2=0[/latex] [latex]( \frac{2}{3} )^{x}=t, t\ \textgreater \ 0[/latex] [latex]( \frac{2}{3} )^{2x}= t^{2} [/latex] [latex]3t-5t+2=0[/latex] [latex] t_{1} = \frac{2}{3} [/latex] [latex] ( \frac{2}{3} )^{x} = \frac{2}{3} [/latex] [latex]x=1[/latex] [latex] t_{2} =1[/latex] [latex]( \frac{2}{3} )^{x} =(\frac{2}{3}) ^{0} [/latex] [latex]x=0[/latex] [latex] x_{1}=0 , x_{2} =1[/latex] 4)[latex]125* 5^{2x}-70*(2*5)^{x} +8* 2^{2x}=0 |/ 5^{2x} [/latex] [latex]125-70*( \frac{2}{5} )^{x}+8* ( \frac{2}{5} )^{2x} =0[/latex] [latex]( \frac{2}{5} )^{x}=t, t\ \textgreater \ 0[/latex] [latex]( \frac{2}{5} )^{2x}= t^{2} [/latex] [latex]8 t^{2}-70t+125=0 [/latex] [latex]t_{1} = \frac{5}{2}[/latex] [latex]( \frac{2}{5} )^{x} = (\frac{2}{5}) ^{-1} [/latex] [latex]x=-1[/latex] [latex]t_{2} = \frac{25}{4}[/latex] [latex]( \frac{2}{5} )^{x} = (\frac{2}{5}) ^{-2} [/latex] [latex]x=-2[/latex] [latex]x_{1}=-2 , x_{2} =-1[/latex]