若a=2^0.5,b=logπ(3),c=log2(sin2π/5).比较大小

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若a=2^0.5,b=logπ(3),c=log2(sin2π/5).比较大小
若a=2^0.5,b=logπ(3),c=log2(sin2π/5).比较大小

若a=2^0.5,b=logπ(3),c=log2(sin2π/5).比较大小
由于2 > 1,则a > 1
3 < π,则b > 0 且 b < 1
sin2π/5 > 0 且 sin2π/5 < 1,则c < 0
故a > b > c

a=√2>1.
b=logπ(3)=lg3/lgπ<1.
c=log2(sin2π/5)=[(lgsin2π/5)/lg2]<0.
∴a>b>c.

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