题目内容
设函数f(x)=logax(a>0且a≠1),若f(x1x2…x2010)=8,则f(x12)+f(x22)+…+f(x20102)=( )
| A.4 | B.8 | C.16 | D.2loga8 |
∵f(x)=logax(a>0,a≠1),且f(x1x2…x2010)=8,
∴f(x12)+f(x22)+…+f(x20102)
=logax12+logax22+…+logax20102
=loga(x1x2…x2010)2
=2f(x1x2…x2010)=2×8=16.
故选C
∴f(x12)+f(x22)+…+f(x20102)
=logax12+logax22+…+logax20102
=loga(x1x2…x2010)2
=2f(x1x2…x2010)=2×8=16.
故选C
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