若tana=2log3(x),tanb=3log1/3(x),a-b=π/4,求x

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若tana=2log3(x),tanb=3log1/3(x),a-b=π/4,求x
若tana=2log3(x),tanb=3log1/3(x),a-b=π/4,求x

若tana=2log3(x),tanb=3log1/3(x),a-b=π/4,求x
tan(a-b)=(tana-tanb)/(1+tanatanb)
=[2log3(x)-3log1/3(x)]/(1+2log3(x)3log1/3(x))
=5log3(x)/(1-6log²3(x))=1
1-6log²3(x)=5log3(x)
6log²(x)+5log3(x)-1=0
[6log3(x)-1][log3(x)+1]=0
log3(x)=1/6 或log3(x)=-1
所以x=3^(1/6) 或 x=3^-1=1/3