解不等式log1/2(x+2)《2log2 1/x

问题描述:

解不等式log1/2(x+2)《2log2 1/x

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

log1/2(x+2)