函数f（x）=loga（x-1）+1（a＞0且a≠1）的图象恒过点A，若点A在直线mx-y+n=0上，则4m+2n的最小值为______．
由题意，函数f（x）的图象恒过（2，1）即A（2，1），故2m+n=1．
∴4m+2n≥2
=2 4m•2n
=2 22m+n
．2
当且仅当4m=2n，即2m=n，
即n=
，m=1 2
时取等号．1 4
∴4m+2n的最小值为2
．2
故答案为：2 2
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| Many people think the 1 time is spent, the more work will be done. So students have to spend the whole day doing school work 2 the three meals. Modern students have many 3 . They love sports, computers and music. A 4 holiday can get them away from too much school work, and they can do what they like. But still teachers do not 5 it. Because they have too much homework, they have no time to enjoy themselves. Students are really tired of their weekend homework. So they don't do it 6 Sunday night. And there is not enough time to finish the homework carefully. The poor weekend homework usually makes teachers 7 . Things always get worse 8 right ideas. Too much school work makes students lose 9 in learning. It's also bad for their health. A horse runs faster after a rest. But for students only a rest is not enough. So such a condition (状况) should be 10 to give students both pleasure and knowledge. | ||||
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