log6(7)=a,log3(4)=b,求log14(21)

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log6(7)=a,log3(4)=b,求log14(21)
log6(7)=a,log3(4)=b,求log14(21)

log6(7)=a,log3(4)=b,求log14(21)
lg7/lg6=a
lg4/lg3=b
所以lg3*b=lg4=2lg2
原式lg21/lg14
=(lg3+lg7)/(lg2+lg7)
=(lg3+lg7)/(lg3*b/2+lg6*a)
=[2lg3+2a(lg2+lg3)]/[lg3*b+2a(lg2+lg3)]
=[(2+2a)lg3+2a*lg2]/[(b+2a)lg3+2a*lg2]
=[(2+2a)2lg2/b+2alg2]/[(n+2a)2lg2/b+2alg2]
=[(2+2a)/b+a]/[(b+2a)/b+a]
=(2+2a+ab)/(b+2a+ab)