解不等式log1/2(x+2)《2log2 1/x

解不等式log1/2(x+2)《2log2 1/x
解不等式log1/2(x+2)《2log2 1/x

解不等式log1/2(x+2)《2log2 1/x
log1/2(x+2)

lg(x+2)/lg(1/2)<2lg(1/x)/lg2
lg(x+2)/(-lg2)<2(-lgx)/lg2
两边乘-lg2
lg(x+2)>2lgx
lg(x+2)>lgx²
x+2>x²
x²-x-2=(x+1)(x-2)<0
-1真数大于0
x+2>0,1/x>0
所以x>0
所以0