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(log2 3+log4 27)(log3 4+log9 8)

亲,若满意该答案请采纳吧!!谢谢!!

3/2

(log2 3+log4 9)(log3 4+log9 2) =[log(2)3+4log(2)3][2log(3)2+2log(3)2] =5log(2)3x4log(3)2 =20

A=m^k,B=n^k,则logA(B)=logm(n) 8^(1/n)=(2*2*2)^(1/n)=2^(3/n),故 log2(8^(1/n))=3/n 所以 log2(3)+log4(9)+log8(27)+…+log(2^n)(3^n)=n*log2(3) 所以 (log2(3)+log4(9)+log8(27)+…+log(2^n)(3^n))*log2(8^(1/n))=3*log2(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

loga(b)*logb(c)=loga(c); loga(b)*logb(c)*logc(d)=loga(d). log2(3)*log3(4)*log4(5)*log5(6)*log6(7)*log7(8)=log2(8)=3,所以3=loga(b),所以b=a^3

原式=(lg3/lg4+lg3/lg8)(lg2/lg3+lg2/lg9)-log2^4-log2^(√32)=(lg3/2lg2+lg3/3lg2)(lg2/lg3+lg2/2lg3)-2-5/2=(1/2+1/3)(lg3/lg2)(1+1/2)(lg2/lg3)-2-5/2=(5/6)×(3/2)-2-5/2=5/4-2-5/2=-13/4

log2(9*27^0.5)+log2 6-log2 3+log4 3*log3 16 =log2(3^4.5)+log2 3-1 2-log2 3+lg3/lg4*lg16/lg3 =4.5log2 3-1+lg16/lg4 =4.5log2 3-1+2 =4.5log2 3+1

(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

原式=(1/2*log2^3+1/3*log2^3)(log3^2+1/2*log3^2) =(5/6*log2^3) * (3/2*log3^2) ={5/6*(lg3)/(lg2)} * {3/2*(lg2/lg3)} =5/4 答案对吗??我很久没做这种题了 ~~~

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