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(log2 6)×(log3 6)%(log2 3+log3 2)=

log2(3)-log4(6) = log2(3)-log2^2((√6)^2) = log2(3)-log2(√6) = log2(3/√6) = log2(√3/√2) = log2(√3)-log2(√2) = 1/2log2(3) - 1/2 如果题目是【log2(3)-log4(36)】 log2(3)-log4(36) = log2(3)-log2^2((6)^2) = log2(3)-log2(6) = log2(3/6)...

log2^6 * log3^6 - log2^3*log3^2 =6 * log2 * 6 * log3 - 3 * log2 * 2 * log3 =30log6

(log3 2+log9 2)*(log4 3+log8 3) =(lg2/lg3+lg2/lg9)*(lg3/lg4+lg3/lg8) =(lg2/lg3+lg2/2lg3)*(lg3/2lg2+lg3/3lg2 =3/2*lg2/lg3*5/6*lg3/lg2 =3/2*5/6=5/4

设所有等式的值为t 所以a=2^(t-2) b=3^(t-3) a+b=6^t 所以1/a+1/b=(a+b)/ab=6^t/[2^(t-2)*3^(t-3)]=6^t/[(2^t)/4*(3^t)/27]=108

请采纳

俊狼猎英团队为您解答 已知lg2=a,lg3=b, log3 4=lg4/lg3=2lg2/lg3=2a/b, log2 12=log2 (2^2×3)=2+log2 3=2+lg3/lg2=2+b/a。 前面部分意思不懂。

你参考看看!

换底公式:loga b=(logc b)/(logc a) 所以log2 36=(log6 36)/(log6 2) log3 36=(log6 36)/(log6 3)

(log3 2+log9 2)*(log4 3+log8 3) =(lg2/lg3+lg2/lg9)*(lg3/lg4+lg3/lg8) =(lg2/lg3+lg2/2lg3)*(lg3/2lg2+lg3/3lg2 =3/2*lg2/lg3*5/6*lg3/lg2 =3/2*5/6=5/4

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