Question

4,6 пожалуйста с проверкой

Answer 1

4)

$\displaystyle log_2(x^2-4x+4)=4\\\\\left \{ {{x^2-4x+4 > 0} \atop {x^2-4x+4=2^4}} \right. \\\\\left \{ {{(x-2)^2 > 0} \atop {x^2-4x+4-16=0}} \right.\\\\\left \{ {{x\neq 2} \atop {x^2-4x-12=0}} \right.\\\\x^2-4x-12=0\\\\D=16+48=64\\\\x_{1.2}=\frac{4 \pm8}{2}\\\\x_1=6; x_2=-2$

проверка:

$\displaystyle log_2(6-2)^2=log_24^2=log_22^4=4\\\\log_2(-2-2)^2=log_24^2=4$

6)

$\displaystyle log_4\frac{4+2x}{x-5}=2\\\\\left \{ {{x-5\neq 0; \frac{4+2x}{x-5} > 0} \atop {\frac{4+2x}{x-5}=4^2}} \right. \\\\\left \{ {{x\neq 5; x\in (-oo;-2)(5;+oo)} \atop {4+2x=16(x-5)}} \right. \\\\4+2x-16(x-5)=0\\\\4+2x-16x+80=0\\\\-14x+84=0\\\\x=6$

проверка

$\displaystyle log_4\frac{4+2*6}{6-5}=log_4\frac{16}{1}=2$