解对数不等式log2 x>(log1/4 x)+3

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解对数不等式log2 x>(log1/4 x)+3
解对数不等式
log2 x>(log1/4 x)+3

解对数不等式log2 x>(log1/4 x)+3
log1/4 x=lgx/lg(1/4)=lgx/lg2^(-2)=lgx/(-2lg2)=(-1/2)log2(x)
所以log2(x)>(-1/2)log2(x)+3
(3/2)log2(x)>3
log2(x)>2=log2(4)
底数2>1
所以log2(x)是增函数
所以x>4

log2x-1/2log2x^-1>3
log2(x/(x^-1/2))>3
log2x^3/2>3
x^3/2>8
x>4

log2(x)>log1/4(x)+3
log2(x)>log2^-2(x)+3
log2(x)>-1/2log2(x)+3
log2(x)+1/2log2(x)>3
3/2log2(x)>3
log2(x)>2
∴x>4