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log2(3)*log3(4)=?

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

Log3(4)=lg4/lg3=2lg2/lg3=2x0.3010/0.4771=1.2617899811≈1.262

log2(3)*log3(4)*log4(5)*log5(6)*log6(7)*log7(8) =(lg3/lg2)(lg4/lg3(*....lg8/lg7; =lg8/lg2=log2(8)=3

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

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。

log2 3 · log3 4 ·log4 5 ·log5 2 =lg3/lg2 * lg4/lg3 * lg5/lg4 * lg2/lg5 =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

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)

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

(log2^3+log4^9)(log3^4+log9^2)= (3*log2+18*log2)(4*log3+4*log3)= 21*log2*8*log3=168log5

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