Question

求方程:log(1/2)(｜x+2｜)=log(2)(｜x-2｜)-2

Answer 1

左边=lg|x+2|/lg(1/2)=lg|x+2|/(-lg2)=-log2(|x+2|)=log2(|x+2|)^(-1)

右边=log2(|x-2|)-log2(4)=log2(|x-2|/4)

所以(|x+2|)^(-1)=|x-2|/4

1/|x+2|=|x-2|/4

|(x+2)(x-2)|=4

|x²-4|=4

x²-4=±4

x²=8,x²=0

x=±2√2,x=0