Задача 43632 ...

azot

2020-01-23 19:48:22

11*4^(log₄²(x-1)) -3(x-1)^(log₄(x-1)²) = -4

sova

2020-01-23 21:13:04

★

[m]4^{log^2_{4}(x-1)}=4^{log_{4}(x-1)\cdot log_{4}(x-1)}=4^{n\cdot n}=(4^{n})^{n}=(4^{log_{4}(x-1)})^{log_{4}(x-1)}=[/m]

[m]a^{log_{a}b}=b\Rightarrow 4^{log_{4}(x-1)}=x-1[/m]

[m](x-1)^{log_{4}(x-1)^2}=(x-1)^{2log_{4}(x-1)}=((x-1)^{log_{4}(x-1)})^{2}[/m]


Уравнение сводится к квадратному

11t-3t^2=-4