log2(3)=a,log4(12),log6(9 - 知识问答

log2(3)=a,log4(12),log6(9),以2为底3的对数是a,求以4为底12的对数,以6为底9的对数,用a

3个回答

a=lg3/lg2
lg3=alg2
log4(12)
=lg12/lg4
=lg(2^2*3)/lg2^2
=(2lg2+lg3)/2lg2
=(2lg2+alg2)/2lg2
=(2+a)/2
log6(9)
=lg9/lg6
=lg3^2/lg2*3
=2lg3/(lg2+lg3)
=2alg2/(lg2+alg2)
=2a/(1+a)

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