Решите уравнение : 27*(4/9)^x-30*(2/3)^x+8=0

[latex]27*( \frac{4}{9} )^x-30*( \frac{2}{3} )^x+8=0[/latex] [latex]27* ( \frac{2}{3} )^{2x} -30*( \frac{2}{3} )^x+8=0[/latex] Замена:    [latex]( \frac{2}{3} )^x=a,[/latex]  [latex]a\ \textgreater \ 0[/latex] [latex]27a^2-30a+8=0[/latex] [latex]D=(-30)^2-4*27*8=900-864=36[/latex] [latex]a_1= \frac{30-6}{54}= \frac{24}{54} = \frac{4}{9} [/latex] [latex]a_2= \frac{30+6}{54}= \frac{36}{54} = \frac{2}{3} [/latex] [latex] (\frac{2}{3})^x = \frac{4}{9} [/latex]     или     [latex] (\frac{2}{3})^x = \frac{2}{3} [/latex] [latex] (\frac{2}{3})^x =( \frac{2}{3} )^2 [/latex] или     [latex] (\frac{2}{3})^x = (\frac{2}{3} )^1 [/latex] [latex]x=2[/latex]           или     [latex]x=1[/latex] Ответ: 1; 2

(4/9)^x=(2/3)^2x делаем замену: y=(2/3)^x 27y^2-30y+8=0 D=36; y1=30+6/54=36/54=4/6=2/3 y2=24/54=4/9 (2/3)^x=2/3 x=1 (2/3)^x=4/9 (2/3)^x=(2/3)^2 x=2 Ответ: x1=1; x2=2