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log2(3)*log3(4)=?

log2(3)*log3(4)=log2(3)*log2(4)/log2(3)=log2(4)=2

您好: 是+号吧 log2(3/4)+log2(4/3) =log2(3/4x4/3) =log2(1) =0 如果本题有什么不明白可以追问,如果满意请点击右下角“采纳为满意回答” 如果有其他问题请采纳本题后另发点击向我求助,答题不易,请谅解,谢谢。 祝学习进步!

(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

log4(15)+log5(4) =log4(3)+log4(5)+log5(4) ≥log4(3)+2√[log4(5)*log5(4)] =log4(3)+2, log2(3)+log3(8)+log4(3) =3/2log2(3)+3log3(2) ≥2√[3/2log2(3)*3log3(20)] =3√2, ∴原式≥3√2+2>6。

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 3 · log3 4 ·log4 5 ·log5 2 =lg3/lg2 * lg4/lg3 * lg5/lg4 * lg2/lg5 =1

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)

1、log2 3*log3 4*log4 5*log5 2 =lg2/lg3xlg3/lg4xlg4/lg5xlg5/lg2 (换底公式) =1 (约分) 2.(log4 3+log8 3)*(log3 2+log9 2) 中间应为乘号 =(lg3/lg4+lg3/lg8)*(lg2/lg3+lg2/lg9) =(lg3/2lg2+lg3/3lg2)*(lg2/lg3+lg2/2lg3) =[(1/2+1/3)(lg...

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

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