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log2 4+log3 9=

是×还是比大小 ×的话:原式=(lg25/lg2)×(lg4/lg3)×(lg9/lg5) =(2lg5/lg2)×(2lg2/lg3)×(2lg3/lg5) =8 比大小的话:log2 16

log2 4+log3 9=2+2=4.

(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

(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

=(log2 3 +3/2log2 3)(2log3 2+3/2log3 2) =5/2log2 3 ×7/2log3 2 =35/4

都换成以2为底的对数进行比较 log2(3)=log2(根号9) log4(5)=log2(根号5) 3/2=log2(2^(3/2))=log2(根号8) 因为y=log2(x)在(0,+无穷)上为增函数 所以log2(3)>3/2>log4(5)

因为3^2=9

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

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