a>1,b>1,log2(a)*log2(b)=64,求log2(ab)最小值

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a>1,b>1,log2(a)*log2(b)=64,求log2(ab)最小值

a>1,b>1,log2(a)*log2(b)=64,求log2(ab)最小值
a>1,b>1,log2(a)*log2(b)=64,求log2(ab)最小值

a>1,b>1,log2(a)*log2(b)=64,求log2(ab)最小值
a>1,b>1,得 log2(a)>0,log2(b)>0
log2(a)*log(b)=64,则 log2(ab)=log2(a)+log(b)≥2根号64=16
当且仅当log2(a)=log2(b)=8 即 a=b=256 时,取最小值16

log2(ab)=log2(a)+log2(b)>=2根号[log2(a)log2(b)]=2根号64=16
因此当log2(a)=log2(b)时,log2(ab)达到最小值16

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