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log2(3)%log4(6)怎么算

log4(6)=1/2log2(6)=log2(√6)log4(6)

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)...

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)

loga b=lnb/lna -->原式=(ln3/ln2)(ln4/ln3)(ln5/ln4)(ln2/ln5)=1 希望有所帮助

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+log3=log6 如下图所示,是“4”的第一个公式的逆运算

(log4∧3+log4∧2)log6∧2 =[log4^(3×2)]log6^2 =log4^6 log6^2 =lg2/lg4 =1/2

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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