Question

решите уравнение

$<var>2log _ {2}(x-2)+log_{2}(x-4)^4=0</var>$

Answer 1

$<var>2log _ {2}(x-2)+log_{2}(x-4)^4=0\\ log _ {2}(x-2)+log_{2}(x-4)^2=0\\ log _ {2}(x-2)+log_{2}(x-4)^2=log_21\\ (x-2)(x-4)^2=1\\ (x-2)(x^2-8x+16)=1\\ x^3-8x^2+16x-2x^2+16x-32-1=0\\ x^3-10x^2+32x-33=0\\ x=3 </var>$